Pub Date : 2025-01-04DOI: 10.1016/j.padiff.2024.101056
Hasib Khan , Jehad Alzabut , D.K. Almutairi
This paper is analyzing Uranium clusters mathematically as well through artificial intelligence discrete fractional order model of four different phases. The model is classifying the decay into the for with different convergence rates for and and . The model is first analyzed for the mathematical validation including existence criteria and stability results. After these, a mathematical scheme based on the discretization is constructed and is applied to an initial data. The model is solved for the novel solutions and simulations for the fractional order 0.98 with variant parametric values. These results numerical results are then tested and affirmed with best validation performance by the use of artificial intelligence. We have observed a tremendous results of with normal distribution of the clustering data around the zero error.
{"title":"Applications of artificial intelligence for clusters analysis of Uranium decay via a fractional order discrete model","authors":"Hasib Khan , Jehad Alzabut , D.K. Almutairi","doi":"10.1016/j.padiff.2024.101056","DOIUrl":"10.1016/j.padiff.2024.101056","url":null,"abstract":"<div><div>This paper is analyzing Uranium clusters mathematically as well through artificial intelligence discrete fractional order model of four different phases. The model is classifying the decay into the <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for <span><math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span> with different convergence rates <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for <span><math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span> and <span><math><msup><mrow><mi>α</mi></mrow><mrow><mo>⊛</mo></mrow></msup></math></span> and <span><math><mi>β</mi></math></span>. The model is first analyzed for the mathematical validation including existence criteria and stability results. After these, a mathematical scheme based on the discretization is constructed and is applied to an initial data. The model is solved for the novel solutions and simulations for the fractional order 0.98 with variant parametric values. These results numerical results are then tested and affirmed with best validation performance by the use of artificial intelligence. We have observed a tremendous results of <span><math><mrow><mi>R</mi><mo>=</mo><mn>1</mn></mrow></math></span> with normal distribution of the clustering data around the zero error.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101056"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-04DOI: 10.1016/j.padiff.2024.101069
Chouaib Bounkaicha, Karam Allali
In this work, we present a mathematical analysis of a reaction–diffusion susceptible–exposed–infected–recovered model with a time fractional order derivative. The model describes the transmission of infectious diseases among the four compartments using fractional-order differential equations. We take into account the spatial diffusion of each variable. To represent the non-linear force of infection, a saturated incidence function is taken into consideration. First, we prove the well-posedness of the suggested model by demonstrating existence, uniqueness and boundedness of solutions. Next, we give the basic reproduction number and the problem steady states. The global stability of both equilibria is fulfilled using the Lyapunov method. Finally, the numerical simulations are conducted to validate the theoretical findings and highlight the impact of vaccination on reducing the severity of infection, as well as the impact of the fractional derivative order on equilibria stability. It has been demonstrated that the fractional derivative order has no impact on the stability of the equilibria, but it has a big effect on the speed of the convergence towards the steady states. In addition, it is observed that when the diffusion parameters are increased, the peak of infected and exposed individuals also gets maximized.
{"title":"Stability analysis of reaction–diffusion fractional-order SEIR model with vaccination and saturated incidence rate","authors":"Chouaib Bounkaicha, Karam Allali","doi":"10.1016/j.padiff.2024.101069","DOIUrl":"10.1016/j.padiff.2024.101069","url":null,"abstract":"<div><div>In this work, we present a mathematical analysis of a reaction–diffusion susceptible–exposed–infected–recovered <span><math><mrow><mo>(</mo><mi>SEIR</mi><mo>)</mo></mrow></math></span> model with a time fractional order derivative. The model describes the transmission of infectious diseases among the four <span><math><mi>SEIR</mi></math></span> compartments using fractional-order differential equations. We take into account the spatial diffusion of each variable. To represent the non-linear force of infection, a saturated incidence function is taken into consideration. First, we prove the well-posedness of the suggested model by demonstrating existence, uniqueness and boundedness of solutions. Next, we give the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and the problem steady states. The global stability of both equilibria is fulfilled using the Lyapunov method. Finally, the numerical simulations are conducted to validate the theoretical findings and highlight the impact of vaccination on reducing the severity of infection, as well as the impact of the fractional derivative order on equilibria stability. It has been demonstrated that the fractional derivative order has no impact on the stability of the equilibria, but it has a big effect on the speed of the convergence towards the steady states. In addition, it is observed that when the diffusion parameters are increased, the peak of infected and exposed individuals also gets maximized.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101069"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-04DOI: 10.1016/j.padiff.2024.101070
A.M.S. Mahdy , M.A. Abdou , D.Sh. Mohamed
This paper is devoted to study the numerical solution of a system of Quadratic integral equations (SQIEs) in position and time in the space using brand-new orthogonal polynomials described as eighth-kind Chebyshev polynomials (CP8K). Specific kinds of Gegenbauer polynomials are these polynomials. By using the separation of variables technique the SQIEs in position and time transformed to SQIEs in position, then by applying CP8K, consequently, a system of linear algebraic equations (SLAEs) is constructed. The Banach fixed point theorem is employed to demonstrate the existence and uniqueness of the SQIEs solution. Additionally, the solution’s convergence and stability are studied. Some numerical examples are constructed to illustrate the efficiency and applicability of the method. All the computational are obtained by Maple 18 software. Finally, computer simulations can be obtained to demonstrate the mathematical results.
{"title":"Numerical solution and dynamical studies for solving system of Quadratic integral equations","authors":"A.M.S. Mahdy , M.A. Abdou , D.Sh. Mohamed","doi":"10.1016/j.padiff.2024.101070","DOIUrl":"10.1016/j.padiff.2024.101070","url":null,"abstract":"<div><div>This paper is devoted to study the numerical solution of a system of Quadratic integral equations (SQIEs) in position and time in the space <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>×</mo><mi>C</mi><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span> using brand-new orthogonal polynomials described as eighth-kind Chebyshev polynomials (CP8K). Specific kinds of Gegenbauer polynomials are these polynomials. By using the separation of variables technique the SQIEs in position and time transformed to SQIEs in position, then by applying CP8K, consequently, a system of linear algebraic equations (SLAEs) is constructed. The Banach fixed point theorem is employed to demonstrate the existence and uniqueness of the SQIEs solution. Additionally, the solution’s convergence and stability are studied. Some numerical examples are constructed to illustrate the efficiency and applicability of the method. All the computational are obtained by Maple 18 software. Finally, computer simulations can be obtained to demonstrate the mathematical results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101070"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-04DOI: 10.1016/j.padiff.2024.101054
Rehana Naz , Willy Hereman
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent , was investigated by Mason and his collaborators (Magan et al., 2018). The Lie algebra for the model is five-dimensional for the shearing exponent , and it includes translations in time, space, and displacement, as well as time-dependent changes in displacement and a scaling symmetry. Applying Lie’s symmetry method, we compute the optimal system of one-dimensional subalgebras. Using the subalgebras, several reductions and closed-form solutions for the model are obtained both for arbitrary exponent and special case . Furthermore, it is shown that for arbitrary the model has interesting conservation laws which are computed with symbolic software using the scaling symmetry of the given PDE.
{"title":"Lie symmetries, closed-form solutions, and conservation laws of a constitutive equation modeling stress in elastic materials","authors":"Rehana Naz , Willy Hereman","doi":"10.1016/j.padiff.2024.101054","DOIUrl":"10.1016/j.padiff.2024.101054","url":null,"abstract":"<div><div>The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent <span><math><mi>n</mi></math></span>, was investigated by Mason and his collaborators (Magan et al., 2018). The Lie algebra for the model is five-dimensional for the shearing exponent <span><math><mrow><mi>n</mi><mo>></mo><mn>0</mn></mrow></math></span>, and it includes translations in time, space, and displacement, as well as time-dependent changes in displacement and a scaling symmetry. Applying Lie’s symmetry method, we compute the optimal system of one-dimensional subalgebras. Using the subalgebras, several reductions and closed-form solutions for the model are obtained both for arbitrary exponent <span><math><mi>n</mi></math></span> and special case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>. Furthermore, it is shown that for arbitrary <span><math><mrow><mi>n</mi><mo>></mo><mn>0</mn></mrow></math></span> the model has interesting conservation laws which are computed with symbolic software using the scaling symmetry of the given PDE.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101054"},"PeriodicalIF":0.0,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.padiff.2024.101071
A. Wakif
Due to the particular inability of Fourier's and Fick's laws in the realistic quantification of transfer processes that can occur certainly within a flowing biphasic mixture, on the one hand, and the explanation of the memory relaxation features of such a non-homogenous medium, on the other hand, the present scrutinization intends to propose a representative biphasic flow model to reveal the principal demeanors of convectively heated thixotropic nanofluids during their steady two-dimensional flows in the laminar regime over a stretching planar geometry in a Darcy-Forchheimer porous medium under the magnetic impact of an external electromagnetic device. For this purpose, the renovated formulation of Wakif-Buongiorno's model is linked theoretically with the constructive equation of the thixotropic model and the generalized transport laws to describe properly the nanofluid motion, the thermal energy balance, and the nanoparticles’ molar concentration distribution under the assumptions of the boundary layer concept and the passive nanoparticles’ control approach. After numerous simplifications and feasible linearizations, the leading dimensionless system is solved numerically by applying an accurate collocation approach. As the main outcomes, it is noted that the upper thixotropic parameters speed up remarkably the thixotropic nanofluid motion and diminish its temperature locally, whilst reverse dynamical and thermal trends are witnessed for the bigger porosity and magnetic parameters. Further, it is remarked also that the increasing and decreasing changes in the thermal and concentration relaxation parameters don't affect the thixotropic nanofluidic medium dynamically. On the contrary, the rising thermal and concentration relaxation parameters lead to dissimilar thermal impressions, in which a cooling effect is produced within the thixotropic nanofluidic medium when elevating the thermal relaxation parameter, while a slight heating behavior is witnessed for the superior concentration relaxation parameters.
{"title":"Numerical simulation of MHD Sakiadis flows of convectively heated thixotropic nanofluids in a porous medium using revised transport laws and Wakif-Buongiorno's model","authors":"A. Wakif","doi":"10.1016/j.padiff.2024.101071","DOIUrl":"10.1016/j.padiff.2024.101071","url":null,"abstract":"<div><div>Due to the particular inability of Fourier's and Fick's laws in the realistic quantification of transfer processes that can occur certainly within a flowing biphasic mixture, on the one hand, and the explanation of the memory relaxation features of such a non-homogenous medium, on the other hand, the present scrutinization intends to propose a representative biphasic flow model to reveal the principal demeanors of convectively heated thixotropic nanofluids during their steady two-dimensional flows in the laminar regime over a stretching planar geometry in a Darcy-Forchheimer porous medium under the magnetic impact of an external electromagnetic device. For this purpose, the renovated formulation of Wakif-Buongiorno's model is linked theoretically with the constructive equation of the thixotropic model and the generalized transport laws to describe properly the nanofluid motion, the thermal energy balance, and the nanoparticles’ molar concentration distribution under the assumptions of the boundary layer concept and the passive nanoparticles’ control approach. After numerous simplifications and feasible linearizations, the leading dimensionless system is solved numerically by applying an accurate collocation approach. As the main outcomes, it is noted that the upper thixotropic parameters speed up remarkably the thixotropic nanofluid motion and diminish its temperature locally, whilst reverse dynamical and thermal trends are witnessed for the bigger porosity and magnetic parameters. Further, it is remarked also that the increasing and decreasing changes in the thermal and concentration relaxation parameters don't affect the thixotropic nanofluidic medium dynamically. On the contrary, the rising thermal and concentration relaxation parameters lead to dissimilar thermal impressions, in which a cooling effect is produced within the thixotropic nanofluidic medium when elevating the thermal relaxation parameter, while a slight heating behavior is witnessed for the superior concentration relaxation parameters.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101071"},"PeriodicalIF":0.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.padiff.2024.101065
Osama Alkhazaleh
This work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants, MHPM achieves enhanced convergence and precision with minimal computational overhead, overcoming limitations of traditional perturbation techniques. We extend MHPM to solve more intricate nonlinear systems, showcasing its adaptability and robustness through applications to Burgers’ equations and the Brusselator model. These examples highlight MHPM’s utility in accurately resolving dynamic systems with real-world implications, including fluid flows, reaction kinetics, and engineering models, where computational efficiency and solution precision are critical.
{"title":"Modification of Homotopy Perturbation method for addressing systems of PDEs","authors":"Osama Alkhazaleh","doi":"10.1016/j.padiff.2024.101065","DOIUrl":"10.1016/j.padiff.2024.101065","url":null,"abstract":"<div><div>This work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants, MHPM achieves enhanced convergence and precision with minimal computational overhead, overcoming limitations of traditional perturbation techniques. We extend MHPM to solve more intricate nonlinear systems, showcasing its adaptability and robustness through applications to Burgers’ equations and the Brusselator model. These examples highlight MHPM’s utility in accurately resolving dynamic systems with real-world implications, including fluid flows, reaction kinetics, and engineering models, where computational efficiency and solution precision are critical.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101065"},"PeriodicalIF":0.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.padiff.2024.101068
Khuram Rafique , Aisha M. Alqahtani , Ayesha Rehman , Najla A. Mohammed , Ilyas Khan
The present study articulates the various features of Casson nanofluid flow over a rotating disk along Brownian motion and thermophoresis effects. In addition the influences of thermal radiations along with Sore effect are taken in to account. Due to the poor thermal performance of conventional fluids, the nanoliquid has attained great importance in heat transmission phenomenon and other industrial and engineering applications in current era. The motivation behind this study is its significance relevance in various technological and engineering applications. The governing flow equations are transformed into nonlinear ODE's by adopting suitable similarity transformations. The Keller box technique is utilized to find the numerical outcomes of the resulting nonlinear ODE's. Graphs illustrated that how non-dimensional physical factors affect the velocity, temperature and concentration patterns. From graphical results, we found the thermal slip slows down the velocity of the liquid. Moreover, the temperature distribution diminishes with the increment in velocity slip factor.
{"title":"Continuum flow model of MHD Casson nanofluid over a rotating disk with multiple slips","authors":"Khuram Rafique , Aisha M. Alqahtani , Ayesha Rehman , Najla A. Mohammed , Ilyas Khan","doi":"10.1016/j.padiff.2024.101068","DOIUrl":"10.1016/j.padiff.2024.101068","url":null,"abstract":"<div><div>The present study articulates the various features of Casson nanofluid flow over a rotating disk along Brownian motion and thermophoresis effects. In addition the influences of thermal radiations along with Sore effect are taken in to account. Due to the poor thermal performance of conventional fluids, the nanoliquid has attained great importance in heat transmission phenomenon and other industrial and engineering applications in current era. The motivation behind this study is its significance relevance in various technological and engineering applications. The governing flow equations are transformed into nonlinear ODE's by adopting suitable similarity transformations. The Keller box technique is utilized to find the numerical outcomes of the resulting nonlinear ODE's. Graphs illustrated that how non-dimensional physical factors affect the velocity, temperature and concentration patterns. From graphical results, we found the thermal slip slows down the velocity of the liquid. Moreover, the temperature distribution diminishes with the increment in velocity slip factor.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101068"},"PeriodicalIF":0.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.padiff.2024.101047
Muhammad Farman , Evern Hincal , Parvaiz Ahmad Naik , Ali Hasan , Aceng Sambas , Kottakkaran Sooppy Nisar
This study gives us an expression of non-integer order in mathematics via fractional Caputo operator just for the broadcast development of different emotions under emergencies due to any situation or some disease. In this work, we fear the effects of COVID-19 in panic situations, considering incidence data by using power law kernels under a fractal fractional operator. The effects of the emotion that causes COVID-19 are also evaluated locally and globally using stability. Based on the fractional order model of COVID-19 viral infection, equilibrium points devoid of illness, well-posedness, uniqueness, and biological viability of solutions are all demonstrated. The effects of the COVID-19 model’s sensitivity analysis with treatment were also investigated. Unique solution and Picards stability of iterative scheme verified by using the fixed point theory concept. To discover the solution of the fractional order system and evaluate the effect of fractional parameters, an advanced numerical approach is applied. In the simulation, all classes are shown to have convergent properties and to hold their positions over time, which accurately depicts how COVID-19 infection behaves in practice. We find a more comparable outcome when comparing non-integer orders to integer orders, which supports the non-integer order’s position. This model’s tools seem to be reasonably strong and capable of creating the predicted theoretical conditions for the problem.
{"title":"A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic","authors":"Muhammad Farman , Evern Hincal , Parvaiz Ahmad Naik , Ali Hasan , Aceng Sambas , Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2024.101047","DOIUrl":"10.1016/j.padiff.2024.101047","url":null,"abstract":"<div><div>This study gives us an expression of non-integer order in mathematics via fractional Caputo operator just for the broadcast development of different emotions under emergencies due to any situation or some disease. In this work, we fear the effects of COVID-19 in panic situations, considering incidence data by using power law kernels under a fractal fractional operator. The effects of the emotion that causes COVID-19 are also evaluated locally and globally using stability. Based on the fractional order model of COVID-19 viral infection, equilibrium points devoid of illness, well-posedness, uniqueness, and biological viability of solutions are all demonstrated. The effects of the COVID-19 model’s sensitivity analysis with treatment were also investigated. Unique solution and Picards stability of iterative scheme verified by using the fixed point theory concept. To discover the solution of the fractional order system and evaluate the effect of fractional parameters, an advanced numerical approach is applied. In the simulation, all classes are shown to have convergent properties and to hold their positions over time, which accurately depicts how COVID-19 infection behaves in practice. We find a more comparable outcome when comparing non-integer orders to integer orders, which supports the non-integer order’s position. This model’s tools seem to be reasonably strong and capable of creating the predicted theoretical conditions for the problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101047"},"PeriodicalIF":0.0,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01DOI: 10.1016/j.padiff.2024.101067
Iftikhar Hussain , Waqar Azeem Khan , Muhammad Tabrez , M. Waqas , Talib K. Ibrahim , Taoufik Saidani , M.S. Kausar , Nurnadiah Zamri , Barno Abdullaeva , Hakim AL Garalleh
In recent decade, the research in nanotechnology brought the idea of nanofluids which are highly conducting materials. Some important applications of nanofluids are justified in pharmaceutical industry, coolants in vehicles engine, preparation process of various medicines for treatment of fatal diseases like cancer, aircraft industry, latest heat exchangers etc. The ferro particles are special class of nanomaterial which attract variety of interest from the researchers. The objective of current research is to perform the investigation for heat and mass transfer subject to Carreau nanofluid to observe the enhancement of heat transmission phenomena. The induction of magnetic dipole has been observed for thermal transport phenomenon. The flow is causing by stretched surface. A simplified system is obtained by utilizing the dimensionless variables. Physical interpretation of results have been presented. Result showed that temperature profile in presence of ferrofluid fluid boosts up with escalation in thermophoresis parameter, while opposite behavior is noted for power law index. The concentration of ferrofluid showing declining behavior for Schmidt numbers and rises for thermophoresis parameter.
{"title":"A computational framework for Carreau nanomaterial induced by stretchy regime considering Brownian diffusion, viscous dissipation, ferromagnetism and thermophoresis","authors":"Iftikhar Hussain , Waqar Azeem Khan , Muhammad Tabrez , M. Waqas , Talib K. Ibrahim , Taoufik Saidani , M.S. Kausar , Nurnadiah Zamri , Barno Abdullaeva , Hakim AL Garalleh","doi":"10.1016/j.padiff.2024.101067","DOIUrl":"10.1016/j.padiff.2024.101067","url":null,"abstract":"<div><div>In recent decade, the research in nanotechnology brought the idea of nanofluids which are highly conducting materials. Some important applications of nanofluids are justified in pharmaceutical industry, coolants in vehicles engine, preparation process of various medicines for treatment of fatal diseases like cancer, aircraft industry, latest heat exchangers etc. The ferro particles are special class of nanomaterial which attract variety of interest from the researchers. The objective of current research is to perform the investigation for heat and mass transfer subject to Carreau nanofluid to observe the enhancement of heat transmission phenomena. The induction of magnetic dipole has been observed for thermal transport phenomenon. The flow is causing by stretched surface. A simplified system is obtained by utilizing the dimensionless variables. Physical interpretation of results have been presented. Result showed that temperature profile in presence of ferrofluid fluid boosts up with escalation in thermophoresis parameter, while opposite behavior is noted for power law index. The concentration of ferrofluid showing declining behavior for Schmidt numbers and rises for thermophoresis parameter.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101067"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The application of artificial neural network has kept the whole world amazed, as it has flourished its roots to analyse different domains of science and technology. The current article is modelled to bear witness to how the artificial neural network is administered to study heat transfer and fluid flow problems. The model constructed analyses the mixed convective and unsteady flow of micropolar fluid through the microchannel in the presence of activation energy and magnetic field using Buongiorno's model. No slip and convective boundary conditions are employed. The partial differential equation is solved using the finite difference method. The artificial neural network using the Levenberg-Marquardt algorithm with the feed-forward backpropagation method is constructed and trained. The results of the analysis show that the material parameter lowers the fluid's velocity. For higher magnetic effects, the micro-rotation profile maximises at left half and minimises at right half of microchannel. The temperature profile increases with increasing Eckert number and thermophoresis parameter. The reaction rate parameter is a depleting function, while the activation energy parameter is an enhancing function of the solutal profile. The results obtained from the artificial neural network for all 8 scenarios are highly reliable due to its high accuracy, which is pleasantly deliberated by the mean square error values, error histograms, training, and regression graphs of the neural network model. The absolute error analysis carried out is in the range of 10−4 to 10−5. The prominent conclusion from the analysis is that artificial neural network is sophisticated tool to predict the subsequent sequel of fluid flow and heat transport over a long period of time, reducing computational time to solve complicated fluid flow problems.
{"title":"Artificial neural network model using Levenberg Marquardt algorithm to analyse transient flow and thermal characteristics of micropolar nanofluid in a microchannel","authors":"Pradeep Kumar , Felicita Almeida , Ajaykumar AR , Qasem Al-Mdallal","doi":"10.1016/j.padiff.2024.101061","DOIUrl":"10.1016/j.padiff.2024.101061","url":null,"abstract":"<div><div>The application of artificial neural network has kept the whole world amazed, as it has flourished its roots to analyse different domains of science and technology. The current article is modelled to bear witness to how the artificial neural network is administered to study heat transfer and fluid flow problems. The model constructed analyses the mixed convective and unsteady flow of micropolar fluid through the microchannel in the presence of activation energy and magnetic field using Buongiorno's model. No slip and convective boundary conditions are employed. The partial differential equation is solved using the finite difference method. The artificial neural network using the Levenberg-Marquardt algorithm with the feed-forward backpropagation method is constructed and trained. The results of the analysis show that the material parameter lowers the fluid's velocity. For higher magnetic effects, the micro-rotation profile maximises at left half and minimises at right half of microchannel. The temperature profile increases with increasing Eckert number and thermophoresis parameter. The reaction rate parameter is a depleting function, while the activation energy parameter is an enhancing function of the solutal profile. The results obtained from the artificial neural network for all 8 scenarios are highly reliable due to its high accuracy, which is pleasantly deliberated by the mean square error values, error histograms, training, and regression graphs of the neural network model. The absolute error analysis carried out is in the range of 10<sup>−4</sup> to 10<sup>−5</sup>. The prominent conclusion from the analysis is that artificial neural network is sophisticated tool to predict the subsequent sequel of fluid flow and heat transport over a long period of time, reducing computational time to solve complicated fluid flow problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101061"},"PeriodicalIF":0.0,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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