Umbreen Ayub, Shahid Mubeen, Amir Abbas, Aziz Khan, Thabet Abdeljawad
There are several problems in physics, such as kinetic energy equation, wave equation, anomalous diffusion process, and viscoelasticity that are described well in the fractional differential equation form. Therefore, the solutions with elementary solution method cannot be solved and described deliberately with detailed physics of the problems, so these problems are solved with the help of special operators such as Mittag–Leffler (M–L) functions equipped with Riemann–Liouville (R–L) fractional operators. Hence, keeping in view the above-mentioned problems in physics in the current study, the generalized properties are derived M–L functions connected with R–L fractional operators that are investigated in the generalized form. These extended special operators will be used for the solutions of generalized kinetic energy equation. The M–L function is a fundamental special function with a wide range of applications in mathematics, physics, engineering, and various scientific disciplines. Ayub et al. gave the definition of newly extended M–L (p,s,k)left(p,s,k) function. Also, they gave its convergence condition and found several results relevant to that. The purpose of this study is to investigate newly extended M–L function and study its elementary properties and integral transforms such as Whittaker transform and fractional Fourier transform. The R–L fractional operator is a fundamental concept in fractional calculus, a branch of mathematics that generalizes differentiation and integration to non-integer orders. In this study, we discuss the relation of M–L (p,s,k)left(p,s,k)-function and R–L fractional operators. In some cases, fractional calculus is used to describe kinetic energy equations, particularly in systems where fractional derivatives are more appropriate than classical integer-order derivatives. The M–L function can appear as a solution or as a part of the solution to these fractional kinetic energy equations. Also, we gave the generalization of kinetic energy equation and its solution in terms of newly extended M–L function.
物理学中的一些问题，如动能方程、波方程、反常扩散过程和粘弹性等，都可以用分数微分方程的形式很好地描述。因此，用基本求解法无法刻意求解和描述这些问题的详细物理过程，所以这些问题需要借助特殊算子来求解，如配备黎曼-黎奥维尔（R-L）分式算子的米塔格-勒夫勒（M-L）函数。因此，在本研究中，考虑到上述物理学问题，推导出了与 R-L 分数算子相连的 M-L 函数的广义性质，并以广义形式对其进行了研究。这些扩展的特殊算子将用于广义动能方程的求解。M-L 函数是一种基本特殊函数，在数学、物理学、工程学和各种科学学科中有着广泛的应用。Ayub 等人给出了新扩展的 M-L ( p , s , k ) left(p,s,k) 函数的定义。此外，他们还给出了其收敛条件，并发现了一些与此相关的结果。本研究的目的是研究新扩展的 M-L 函数，并研究其基本性质和积分变换，如惠特克变换和分数傅里叶变换。R-L 分数算子是分数微积分的一个基本概念，分数微积分是将微分和积分推广到非整数阶的数学分支。在本研究中，我们讨论了 M-L ( p , s , k ) left(p,s,k) -函数与 R-L 分数算子的关系。在某些情况下，分数微积分用于描述动能方程，特别是在分数导数比经典整数阶导数更合适的系统中。M-L 函数可以作为这些分数动能方程的解或解的一部分出现。此外，我们还给出了动能方程的广义化及其新扩展的 M-L 函数的解。
{"title":"Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function","authors":"Umbreen Ayub, Shahid Mubeen, Amir Abbas, Aziz Khan, Thabet Abdeljawad","doi":"10.1515/phys-2024-0005","DOIUrl":"https://doi.org/10.1515/phys-2024-0005","url":null,"abstract":"There are several problems in physics, such as kinetic energy equation, wave equation, anomalous diffusion process, and viscoelasticity that are described well in the fractional differential equation form. Therefore, the solutions with elementary solution method cannot be solved and described deliberately with detailed physics of the problems, so these problems are solved with the help of special operators such as Mittag–Leffler (M–L) functions equipped with Riemann–Liouville (R–L) fractional operators. Hence, keeping in view the above-mentioned problems in physics in the current study, the generalized properties are derived M–L functions connected with R–L fractional operators that are investigated in the generalized form. These extended special operators will be used for the solutions of generalized kinetic energy equation. The M–L function is a fundamental special function with a wide range of applications in mathematics, physics, engineering, and various scientific disciplines. Ayub <jats:italic>et al.</jats:italic> gave the definition of newly extended M–L <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_phys-2024-0005_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>k</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(p,s,k)</jats:tex-math> </jats:alternatives> </jats:inline-formula> function. Also, they gave its convergence condition and found several results relevant to that. The purpose of this study is to investigate newly extended M–L function and study its elementary properties and integral transforms such as Whittaker transform and fractional Fourier transform. The R–L fractional operator is a fundamental concept in fractional calculus, a branch of mathematics that generalizes differentiation and integration to non-integer orders. In this study, we discuss the relation of M–L <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_phys-2024-0005_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>k</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(p,s,k)</jats:tex-math> </jats:alternatives> </jats:inline-formula>-function and R–L fractional operators. In some cases, fractional calculus is used to describe kinetic energy equations, particularly in systems where fractional derivatives are more appropriate than classical integer-order derivatives. The M–L function can appear as a solution or as a part of the solution to these fractional kinetic energy equations. Also, we gave the generalization of kinetic energy equation and its solution in terms of newly extended M–L function.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"46 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Eugene Oks, Elisabeth Dalimier, Paulo Angelo, Tatiana Pikuz
Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser–plasma interactions. Second, we review analytical results concerning the Stark–Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha π-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures (“L-dips”) in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser–plasma interactions. We also review the rich physics behind the L-dips phenomenon – because there was a confusion in the literature in this regard.
{"title":"Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas","authors":"Eugene Oks, Elisabeth Dalimier, Paulo Angelo, Tatiana Pikuz","doi":"10.1515/phys-2024-0002","DOIUrl":"https://doi.org/10.1515/phys-2024-0002","url":null,"abstract":"Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser–plasma interactions. Second, we review analytical results concerning the Stark–Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha π-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures (“L-dips”) in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser–plasma interactions. We also review the rich physics behind the L-dips phenomenon – because there was a confusion in the literature in this regard.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"39 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mashael M. AlBaidani, Umair Ali, Abdul Hamid Ganie
The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp(−Φ(ξ))(-Phi (xi )) expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.
{"title":"Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions","authors":"Mashael M. AlBaidani, Umair Ali, Abdul Hamid Ganie","doi":"10.1515/phys-2023-0192","DOIUrl":"https://doi.org/10.1515/phys-2023-0192","url":null,"abstract":"The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_phys-2023-0192_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mo>−</m:mo> <m:mi mathvariant=\"normal\">Φ</m:mi> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>ξ</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:tex-math>(-Phi (xi ))</jats:tex-math> </jats:alternatives> </jats:inline-formula> expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"40 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research article analytically investigates a soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences and engineering. The soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences along with engineering, is examined with a view to securing various pertinent results of interest. For the first time, the conserved currents of an integrodifferential equation (especially those of higher dimensions) are calculated using a detailed optimal system of one-dimensional subalgebras. Infinitesimal generators of diverse structures ascribed to Lie point symmetries of the understudy model are first calculated via Lie group analysis technique. Additionally, we construct various commutations along Lie-adjoint representation tables connected to the nine-dimensional Lie algebra achieved. Further to that, detailed and comprehensive computation of the optimal system of one-dimensional subalgebras linked to the algebra is also unveiled for the under-investigated model. This, in consequence, engenders the calculation of abundant conserved currents for the soliton equation through Ibragimov’s conserved vector theorem by utilizing its formal Lagrangian. Later, the applications of our results are highlighted.
{"title":"Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering","authors":"Oke Davies Adeyemo, Chaudry Masood Khalique","doi":"10.1515/phys-2023-0155","DOIUrl":"https://doi.org/10.1515/phys-2023-0155","url":null,"abstract":"This research article analytically investigates a soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences and engineering. The soliton equation of high dimensions, particularly with applications, and precisely in the fields of physical sciences along with engineering, is examined with a view to securing various pertinent results of interest. For the first time, the conserved currents of an integrodifferential equation (especially those of higher dimensions) are calculated using a detailed optimal system of one-dimensional subalgebras. Infinitesimal generators of diverse structures ascribed to Lie point symmetries of the understudy model are first calculated <jats:italic>via</jats:italic> Lie group analysis technique. Additionally, we construct various commutations along Lie-adjoint representation tables connected to the nine-dimensional Lie algebra achieved. Further to that, detailed and comprehensive computation of the optimal system of one-dimensional subalgebras linked to the algebra is also unveiled for the under-investigated model. This, in consequence, engenders the calculation of abundant conserved currents for the soliton equation through Ibragimov’s conserved vector theorem by utilizing its formal Lagrangian. Later, the applications of our results are highlighted.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"26 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chunxia Wang, Xiaojun Yin, Na Cao, Liyang Xu, Shuting Bai
The ZK–mZK–BBM equation plays a crucial role in actually depicting the gravity water waves with the long wave region. In this article, the bilinear forms of the (2 + 1)-dimensional ZK–mZK–BBM equation were derived using variable transformation. Then, the multiple soliton solutions of the ZK–mZK–BBM equation are obtained by bilinear forms and symbolic computation. Under complex conjugate transformations, quasi-soliton solutions and mixed solutions composed of one-soliton and one-quasi-soliton are derived from soliton solutions. These solutions are further studied graphically to observe the propagation characteristics of gravity water waves. The results enrich the research of gravity water wave in fluid mechanics.
{"title":"Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves","authors":"Chunxia Wang, Xiaojun Yin, Na Cao, Liyang Xu, Shuting Bai","doi":"10.1515/phys-2023-0205","DOIUrl":"https://doi.org/10.1515/phys-2023-0205","url":null,"abstract":"The ZK–mZK–BBM equation plays a crucial role in actually depicting the gravity water waves with the long wave region. In this article, the bilinear forms of the (2 + 1)-dimensional ZK–mZK–BBM equation were derived using variable transformation. Then, the multiple soliton solutions of the ZK–mZK–BBM equation are obtained by bilinear forms and symbolic computation. Under complex conjugate transformations, quasi-soliton solutions and mixed solutions composed of one-soliton and one-quasi-soliton are derived from soliton solutions. These solutions are further studied graphically to observe the propagation characteristics of gravity water waves. The results enrich the research of gravity water wave in fluid mechanics.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"142 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Valeriy Astapenko, Timur Bergaliyev, Sergey Sakhno
This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.
{"title":"Pulsed excitation of a quantum oscillator: A model accounting for damping","authors":"Valeriy Astapenko, Timur Bergaliyev, Sergey Sakhno","doi":"10.1515/phys-2023-0208","DOIUrl":"https://doi.org/10.1515/phys-2023-0208","url":null,"abstract":"This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"3 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Makosha Ishmaeline Charlotte Morakaladi, Abdon Atangana
This work deals with the conversion of flow from confined to unconfined aquifers, a real-world problem that has attracted the attention of several authors. We have introduced a piecewise modified mathematical model where the first part deals with the flow within a confined system, and the second part deals with the flow within an unconfined system. In the unconfined part, we added the randomness to capture stochastic behaviours that could occur due to the geological formation. Moreover, we used a numerical method to solve the stochastic differential equations. The obtained model was evaluated numerically using some numerical scheme, and the stability analysis was performed using the von Neumann approach and the numerical simulations were presented.
{"title":"Model of conversion of flow from confined to unconfined aquifers with stochastic approach","authors":"Makosha Ishmaeline Charlotte Morakaladi, Abdon Atangana","doi":"10.1515/phys-2023-0153","DOIUrl":"https://doi.org/10.1515/phys-2023-0153","url":null,"abstract":"This work deals with the conversion of flow from confined to unconfined aquifers, a real-world problem that has attracted the attention of several authors. We have introduced a piecewise modified mathematical model where the first part deals with the flow within a confined system, and the second part deals with the flow within an unconfined system. In the unconfined part, we added the randomness to capture stochastic behaviours that could occur due to the geological formation. Moreover, we used a numerical method to solve the stochastic differential equations. The obtained model was evaluated numerically using some numerical scheme, and the stability analysis was performed using the von Neumann approach and the numerical simulations were presented.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"27 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mdi Begum Jeelani, Ghaliah Alhamzi, Mian Bahadur Zada, Muhammad Hassan
Variable-order derivatives are the natural extension of ordinary as well as of fractional-order differentiations and integration, respectively. Numerous suggestions for fractional variable-order operators have been made in the literature over time. Therefore, this is the moment to shine a light on the variable-order fractional calculus, due to the fact that it accurately describes the mathematical underpinnings and emphasizing the modeling utility via using contemporary numerical techniques. This study focuses on investigating a fractional variable-order model of lymphatic filariasis infection using with Atangana–Beleanue–Caputo derivative. Our investigations have led to the development of newly refined results, focusing on both qualitative and numerical aspects of analysis. To achieve our research objectives, we employ the fixed point theorems of Banach and Krasnoselskii. These theorems serve as powerful tools, allowing us to establish results regarding the existence of solutions to the model. Additionally, for precise numerical simulations, we employ the fractional Euler’s method, a sophisticated computational technique that allows us to effectively simulate and interpret the results both numerically and graphically. These graphs illustrate distinct variable-orders, providing a comprehensive understanding of the model’s behavior under different conditions. Here, it should be kept in mind that we have select various continuous functions for variable to present our graphical illustration.
{"title":"Study of fractional variable-order lymphatic filariasis infection model","authors":"Mdi Begum Jeelani, Ghaliah Alhamzi, Mian Bahadur Zada, Muhammad Hassan","doi":"10.1515/phys-2023-0206","DOIUrl":"https://doi.org/10.1515/phys-2023-0206","url":null,"abstract":"Variable-order derivatives are the natural extension of ordinary as well as of fractional-order differentiations and integration, respectively. Numerous suggestions for fractional variable-order operators have been made in the literature over time. Therefore, this is the moment to shine a light on the variable-order fractional calculus, due to the fact that it accurately describes the mathematical underpinnings and emphasizing the modeling utility <jats:italic>via</jats:italic> using contemporary numerical techniques. This study focuses on investigating a fractional variable-order model of lymphatic filariasis infection using with Atangana–Beleanue–Caputo derivative. Our investigations have led to the development of newly refined results, focusing on both qualitative and numerical aspects of analysis. To achieve our research objectives, we employ the fixed point theorems of Banach and Krasnoselskii. These theorems serve as powerful tools, allowing us to establish results regarding the existence of solutions to the model. Additionally, for precise numerical simulations, we employ the fractional Euler’s method, a sophisticated computational technique that allows us to effectively simulate and interpret the results both numerically and graphically. These graphs illustrate distinct variable-orders, providing a comprehensive understanding of the model’s behavior under different conditions. Here, it should be kept in mind that we have select various continuous functions for variable to present our graphical illustration.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"2016 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The microscopic pore-fracture structure and wettability have a significant influence on the two-phase seepage of shale gas and water. Due to the limitation of experimental conditions, the seepage patterns of gas and water in shale pores and slits under different wetting conditions have not been clarified yet. In this study, the three-dimensional digital rock models of shale inorganic pores, organic pores, and microfractures are established by focused ion beam-scanning electron microscopy scanning, and gas-driven water seepage simulation in shale microscopic pore-fracture structure under different wetting conditions is carried out based on volume of fluid method. The simulation results show that the gas–water relative permeability curves of microfractures are up-concave, and the gas–water relative permeability curves of inorganic and organic pores are up-convex; the gas–water two-phase percolation in microfractures is least affected by the change of wettability, the gas–water two-phase percolation in inorganic pores is most affected by the change of wettability, and the organic pores are in between; the gas–water two-phase percolation zone of microfractures is the largest, and the isotonic saturation is the highest; under the water-wet conditions, the critical gas saturation of microfractures, inorganic pores, and organic pores are 0.13, 0.315, and 0.34, respectively, and the critical gas saturation of organic pores under non-water-wet conditions is 0.525, indicating that under water-bearing conditions, the shale gas flow capacity in water-wet microfractures is the strongest, followed by water-wet inorganic pores, water-wet organic pores, and hydrophobic organic pores, respectively.
{"title":"Microscopic seepage simulation of gas and water in shale pores and slits based on VOF","authors":"Benqiang Wang, Denglin Han, Wei Lin, Xin Nie, Chenchen Wang, Jizhen Zhang","doi":"10.1515/phys-2023-0166","DOIUrl":"https://doi.org/10.1515/phys-2023-0166","url":null,"abstract":"The microscopic pore-fracture structure and wettability have a significant influence on the two-phase seepage of shale gas and water. Due to the limitation of experimental conditions, the seepage patterns of gas and water in shale pores and slits under different wetting conditions have not been clarified yet. In this study, the three-dimensional digital rock models of shale inorganic pores, organic pores, and microfractures are established by focused ion beam-scanning electron microscopy scanning, and gas-driven water seepage simulation in shale microscopic pore-fracture structure under different wetting conditions is carried out based on volume of fluid method. The simulation results show that the gas–water relative permeability curves of microfractures are up-concave, and the gas–water relative permeability curves of inorganic and organic pores are up-convex; the gas–water two-phase percolation in microfractures is least affected by the change of wettability, the gas–water two-phase percolation in inorganic pores is most affected by the change of wettability, and the organic pores are in between; the gas–water two-phase percolation zone of microfractures is the largest, and the isotonic saturation is the highest; under the water-wet conditions, the critical gas saturation of microfractures, inorganic pores, and organic pores are 0.13, 0.315, and 0.34, respectively, and the critical gas saturation of organic pores under non-water-wet conditions is 0.525, indicating that under water-bearing conditions, the shale gas flow capacity in water-wet microfractures is the strongest, followed by water-wet inorganic pores, water-wet organic pores, and hydrophobic organic pores, respectively.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"100 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140169214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ebrahem A. Algehyne, Showkat Ahmad Lone, Anwar Saeed, Gabriella Bognár
This article presented micropolar hybrid nanofluid flow comprising copper and alumina nanoparticles over a flat sheet. The mixed convection phenomenon is studied under the effect of gravity. Some additional forces such as magnetic field, thermal radiation, Eckert number, heat source, and thermal slip condition are adopted in this analysis. The leading equations are transformed into dimensionless format by employing appropriate variables and then evaluated by homotopy analysis method (HAM). The obtained results are compared with published results and found a good agreement with those published results. Also, the results of HAM are compared with those of numerical method and found a good agreement as well. The fluctuations within the flow profiles are showcased utilizing figures and tables, followed by an in-depth discussion and analysis. The outcomes of this work show that the higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid viscosity, which results in the augmenting variation in the velocity profiles. The higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid thermal conductivity, which results in the augmenting variation in thermal distribution. The growing mixed convection factor amplifies the buoyancy force toward the stagnation point flow, which enlarges the velocity panel. The effects of hybrid nanoparticles (Cu-Al2O3/water) at the surface are smaller on friction force and larger in case of thermal flow rate when compared to the nanofluids (Cu/water and Al2O3/water).
{"title":"Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface","authors":"Ebrahem A. Algehyne, Showkat Ahmad Lone, Anwar Saeed, Gabriella Bognár","doi":"10.1515/phys-2023-0201","DOIUrl":"https://doi.org/10.1515/phys-2023-0201","url":null,"abstract":"This article presented micropolar hybrid nanofluid flow comprising copper and alumina nanoparticles over a flat sheet. The mixed convection phenomenon is studied under the effect of gravity. Some additional forces such as magnetic field, thermal radiation, Eckert number, heat source, and thermal slip condition are adopted in this analysis. The leading equations are transformed into dimensionless format by employing appropriate variables and then evaluated by homotopy analysis method (HAM). The obtained results are compared with published results and found a good agreement with those published results. Also, the results of HAM are compared with those of numerical method and found a good agreement as well. The fluctuations within the flow profiles are showcased utilizing figures and tables, followed by an in-depth discussion and analysis. The outcomes of this work show that the higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid viscosity, which results in the augmenting variation in the velocity profiles. The higher volume fractions of copper and alumina nanoparticles improved the hybrid nanofluid thermal conductivity, which results in the augmenting variation in thermal distribution. The growing mixed convection factor amplifies the buoyancy force toward the stagnation point flow, which enlarges the velocity panel. The effects of hybrid nanoparticles (Cu-Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub>/water) at the surface are smaller on friction force and larger in case of thermal flow rate when compared to the nanofluids (Cu/water and Al<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub>/water).","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"70 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140148259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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