Pub Date : 2023-04-27DOI: 10.15388/namc.2023.28.32127
A. Subramanyam Reddy, S. Rajamani, Ali J. Chamkha, Sunitha C. Srinivas, K. Jagadeshkumar
This article studies the magnetohydrodynamic flow of non-Newtonian ferro nanofluid subject to time-dependent pressure gradient between two vertical permeable walls with Cattaneo–Christov heat flux and entropy generation. In this study, blood is considered as non-Newtonian fluid (couple stress fluid). Nanoparticles’ shape factor, Joule heating, viscous dissipation, and radiative heat impacts are examined. This investigation is crucial in nanodrug delivery, pharmaceutical processes, microelectronics, biomedicines, and dynamics of physiological fluids. The flow governing partial differential equations are transformed into the system of ordinary differential equations by deploying the perturbation process and then handled with Runge–Kutta 4th-order procedure aided by the shooting approach. Hamilton–Crosser model is employed to analyze the thermal conductivity of different shapes of nanoparticles. The obtained results reveal that intensifying Eckert number leads to a higher temperature, while the reverse is true for increased thermal relaxation parameter. Heat transfer rate escalates for increasing thermal radiation. Entropy dwindles for intensifying thermal relaxation parameter.
{"title":"MHD flow of non-Newtonian ferro nanofluid between two vertical porous walls with Cattaneo–Christov heat flux, entropy generation, and time-dependent pressure gradient","authors":"A. Subramanyam Reddy, S. Rajamani, Ali J. Chamkha, Sunitha C. Srinivas, K. Jagadeshkumar","doi":"10.15388/namc.2023.28.32127","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32127","url":null,"abstract":"This article studies the magnetohydrodynamic flow of non-Newtonian ferro nanofluid subject to time-dependent pressure gradient between two vertical permeable walls with Cattaneo–Christov heat flux and entropy generation. In this study, blood is considered as non-Newtonian fluid (couple stress fluid). Nanoparticles’ shape factor, Joule heating, viscous dissipation, and radiative heat impacts are examined. This investigation is crucial in nanodrug delivery, pharmaceutical processes, microelectronics, biomedicines, and dynamics of physiological fluids. The flow governing partial differential equations are transformed into the system of ordinary differential equations by deploying the perturbation process and then handled with Runge–Kutta 4th-order procedure aided by the shooting approach. Hamilton–Crosser model is employed to analyze the thermal conductivity of different shapes of nanoparticles. The obtained results reveal that intensifying Eckert number leads to a higher temperature, while the reverse is true for increased thermal relaxation parameter. Heat transfer rate escalates for increasing thermal radiation. Entropy dwindles for intensifying thermal relaxation parameter.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47482888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-27DOI: 10.15388/namc.2023.28.31801
Renu Chaudhary, S. Reich
We present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. We prove our results by applying bounded integral contractors and a sequencing technique. In contrast to the papers available in the literature, in order to establish our controllability results, we need not define the induced inverse of the controllability operator, and the pertinent nonlinear function need not necessarily satisfy a Lipschitz condition. In addition, we also establish trajectory controllability results. Finally, we discuss an application, which illustrates our results.
{"title":"On the solvability of the Atangana–Baleanu fractional evolution equations: An integral contractor approach","authors":"Renu Chaudhary, S. Reich","doi":"10.15388/namc.2023.28.31801","DOIUrl":"https://doi.org/10.15388/namc.2023.28.31801","url":null,"abstract":"We present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. We prove our results by applying bounded integral contractors and a sequencing technique. In contrast to the papers available in the literature, in order to establish our controllability results, we need not define the induced inverse of the controllability operator, and the pertinent nonlinear function need not necessarily satisfy a Lipschitz condition. In addition, we also establish trajectory controllability results. Finally, we discuss an application, which illustrates our results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48371982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-27DOI: 10.15388/namc.2023.28.32130
Jiafa Xu, Jie Liu, D. O’Regan
In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results.
{"title":"Solvability for a Hadamard-type fractional integral boundary value problem","authors":"Jiafa Xu, Jie Liu, D. O’Regan","doi":"10.15388/namc.2023.28.32130","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32130","url":null,"abstract":"In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49619370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-26DOI: 10.15388/namc.2023.28.32123
S. Smirnov
We study the existence of multiple positive solutions for a nonlinear third-order differential equation subject to various nonlocal boundary conditions. The boundary conditions that we study contain Stieltjes integral and include the special cases of m-point conditions and integral conditions. The main tool in the proof of our result is Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider examples.
{"title":"Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions","authors":"S. Smirnov","doi":"10.15388/namc.2023.28.32123","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32123","url":null,"abstract":"We study the existence of multiple positive solutions for a nonlinear third-order differential equation subject to various nonlocal boundary conditions. The boundary conditions that we study contain Stieltjes integral and include the special cases of m-point conditions and integral conditions. The main tool in the proof of our result is Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider examples.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47818011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-26DOI: 10.15388/namc.2023.28.32118
Murugesan Johnson, K. Kavitha, D. Chalishajar, Muslim Malik, V. Vijayakumar, A. Shukla
This study focused on the approximate controllability results for the Hilfer fractional delay evolution equations of the Sobolev type without uniqueness. Initially, the Lipschitz condition is derived from the hypothesis, which is represented by a measure of noncompactness, in particular, nonlinearity. We also examined the continuity of the solution map of the Sobolev type of Hilfer fractional delay evolution equation and the topological structure of the solution set. Furthermore, we prove the approximate controllability of the fractional evolution equation of the Sobolev type with delay. Finally, we provided an example to illustrate the theoretical results.
{"title":"An analysis of approximate controllability for Hilfer fractional delay differential equations of Sobolev type without uniqueness","authors":"Murugesan Johnson, K. Kavitha, D. Chalishajar, Muslim Malik, V. Vijayakumar, A. Shukla","doi":"10.15388/namc.2023.28.32118","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32118","url":null,"abstract":"This study focused on the approximate controllability results for the Hilfer fractional delay evolution equations of the Sobolev type without uniqueness. Initially, the Lipschitz condition is derived from the hypothesis, which is represented by a measure of noncompactness, in particular, nonlinearity. We also examined the continuity of the solution map of the Sobolev type of Hilfer fractional delay evolution equation and the topological structure of the solution set. Furthermore, we prove the approximate controllability of the fractional evolution equation of the Sobolev type with delay. Finally, we provided an example to illustrate the theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42312055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-26DOI: 10.15388/namc.2023.28.32119
Parvaneh Lo’lo’, M. Shams, M. de La Sen
In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation.
{"title":"Existence of a solution for a nonlinear integral equation by nonlinear contractions involving simulation function in partially ordered metric space","authors":"Parvaneh Lo’lo’, M. Shams, M. de La Sen","doi":"10.15388/namc.2023.28.32119","DOIUrl":"https://doi.org/10.15388/namc.2023.28.32119","url":null,"abstract":"In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function in a partially ordered metric space. For this pair of operators with and without continuity, we derive some results about the coincidence and unique common fixed point. In the following, many known and dependent consequences in fixed point theory in a partially ordered metric space are deduced. As well, we furnish two interesting examples to explain our main consequences, so that one of them does not apply to the principle of Banach contraction. Finally, we use our consequences to create a solution for a particular type of nonlinear integral equation.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44885226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-12DOI: 10.15388/namc.2023.28.31958
Min Zhu, Tingting Feng, Yong Xu, Jinde Cao
The changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number R0, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if R0 ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if R0 > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simul., 155:115–129, 2019] in which some dynamical results have been studied only on the cases R0 < 1 and R0 > 1. Our results not only include the scenario on the case R0 = 1, but also involve the more succinct conditions on the cases R0 < 1 and R0 > 1.
{"title":"Global dynamics of a dengue fever model incorporating transmission seasonality","authors":"Min Zhu, Tingting Feng, Yong Xu, Jinde Cao","doi":"10.15388/namc.2023.28.31958","DOIUrl":"https://doi.org/10.15388/namc.2023.28.31958","url":null,"abstract":"The changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number R0, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if R0 ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if R0 > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simul., 155:115–129, 2019] in which some dynamical results have been studied only on the cases R0 < 1 and R0 > 1. Our results not only include the scenario on the case R0 = 1, but also involve the more succinct conditions on the cases R0 < 1 and R0 > 1.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45612474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.15388/namc.2023.28.31878
Xiangnian Yin, Hongmei Zhang, Hai Zhang, Weiwei Zhang, Jinde Cao
This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations.
{"title":"New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks","authors":"Xiangnian Yin, Hongmei Zhang, Hai Zhang, Weiwei Zhang, Jinde Cao","doi":"10.15388/namc.2023.28.31878","DOIUrl":"https://doi.org/10.15388/namc.2023.28.31878","url":null,"abstract":"This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49359812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-29DOI: 10.15388/namc.2023.28.31866
M. S. Iqbal, M. Inc., S. Sohail, Hina Khurshid, Kalsoom Chishti
In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.
{"title":"Analysis and soliton solutions of biofilm model by new extended direct algebraic method","authors":"M. S. Iqbal, M. Inc., S. Sohail, Hina Khurshid, Kalsoom Chishti","doi":"10.15388/namc.2023.28.31866","DOIUrl":"https://doi.org/10.15388/namc.2023.28.31866","url":null,"abstract":"In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47493128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, based on the properties of Green function and the eigenvalue of a corresponding linear operator, the existence of positive solutions is investigated by spectral analysis for a infinite-points singular p-Laplacian Hadamard fractional differential equation boundary value problem, and an example is given to demonstrate the validity of our main results.
{"title":"Existence of positive solutions for singular p-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term","authors":"Limin Guo, Haimei Liu, Cheng Li, Jing Zhao, Jiafa Xu","doi":"10.15388/namc.2023.28.31728","DOIUrl":"https://doi.org/10.15388/namc.2023.28.31728","url":null,"abstract":"In this paper, based on the properties of Green function and the eigenvalue of a corresponding linear operator, the existence of positive solutions is investigated by spectral analysis for a infinite-points singular p-Laplacian Hadamard fractional differential equation boundary value problem, and an example is given to demonstrate the validity of our main results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43623169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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