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Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid 使用非均匀网格的分数Euler和Runge–Kutta方法的广义形式
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-08 DOI: 10.1515/ijnsns-2021-0278
Pushpendra Kumar, V. S. Erturk, M. Murillo‐Arcila, C. Harley
{"title":"Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid","authors":"Pushpendra Kumar, V. S. Erturk, M. Murillo‐Arcila, C. Harley","doi":"10.1515/ijnsns-2021-0278","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0278","url":null,"abstract":"Abstract In this article, we propose generalized forms of three well-known fractional numerical methods namely Euler, Runge–Kutta 2-step, and Runge–Kutta 4-step, respectively. The new versions we provide of these methods are derived by utilizing a non-uniform grid which is slightly different from previous versions of these algorithms. A new generalized form of the well-known Caputo-type fractional derivative is used to derive the results. All necessary analyses related to the stability, convergence, and error bounds are also provided. The precision of all simulated results is justified by performing multiple numerical experiments, with some meaningful problems solved by implementing the code in Mathematica. Finally, we give a brief discussion on the simulated results which shows that the generalized methods are novel, effective, reliable, and very easy to implement.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48381884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Controllability of coupled fractional integrodifferential equations 耦合分数阶积分微分方程的可控性
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-08 DOI: 10.1515/ijnsns-2022-0015
H. Waheed, A. Zada, R. Rizwan, I. Popa
{"title":"Controllability of coupled fractional integrodifferential equations","authors":"H. Waheed, A. Zada, R. Rizwan, I. Popa","doi":"10.1515/ijnsns-2022-0015","DOIUrl":"https://doi.org/10.1515/ijnsns-2022-0015","url":null,"abstract":"Abstract In this article, we examine a coupled system of fractional integrodifferential equations of Liouville–Caputo form with instantaneous impulsive conditions in a Banach space. We obtain the existence and uniqueness results by applying the theory of fixed point theorems. In a similar manner, we discuss Hyers–Ulam stability and controllability. We also present an example to show the validity of the obtained results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43184722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Analysis and numerical effects of time-delayed rabies epidemic model with diffusion 具有扩散的时滞狂犬病流行模型分析及数值效应
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-07 DOI: 10.1515/ijnsns-2021-0233
Muhammad Jawaz, M. A. Rehman, N. Ahmed, D. Baleanu, M. Iqbal, M. Rafiq, A. Raza
{"title":"Analysis and numerical effects of time-delayed rabies epidemic model with diffusion","authors":"Muhammad Jawaz, M. A. Rehman, N. Ahmed, D. Baleanu, M. Iqbal, M. Rafiq, A. Raza","doi":"10.1515/ijnsns-2021-0233","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0233","url":null,"abstract":"Abstract The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von–Neumann method. Taylor’s expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of τ on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41779436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space 研究了Banach空间中阶r∈(1,2)的分数阶演化内含物的存在性结果
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-07 DOI: 10.1515/ijnsns-2021-0368
M. Mohan Raja, V. Vijayakumar, A. Shukla, K. Nisar, S. Rezapour
{"title":"Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space","authors":"M. Mohan Raja, V. Vijayakumar, A. Shukla, K. Nisar, S. Rezapour","doi":"10.1515/ijnsns-2021-0368","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0368","url":null,"abstract":"Abstract This manuscript investigates the issue of existence results for fractional differential evolution inclusions of order r ∈ (1, 2) in the Banach space. In the beginning, we analyze the existence results by referring to the fractional calculations, cosine families, multivalued function, and Martelli’s fixed point theorem. The result is also used to investigate the existence of nonlocal fractional evolution inclusions of order r ∈ (1, 2). Finally, a concrete application is given to illustrate our main results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45430546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations 非局部耦合复变Korteweg–de Vries方程中的有理孤子解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-07 DOI: 10.1515/ijnsns-2021-0337
Miao Li, Yi Zhang, Rusuo Ye, Yu Lou
{"title":"Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations","authors":"Miao Li, Yi Zhang, Rusuo Ye, Yu Lou","doi":"10.1515/ijnsns-2021-0337","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0337","url":null,"abstract":"Abstract In this article, our work oversees with the nonlocal coupled complex modified Korteweg–de Vries equations (cmKdV), which is a nonlocal generalization for coupled cmKdV equations. The n-fold Darboux transformation (DT) is constructed in the form of determinants for the nonlocal coupled cmKdV equations. Via generalized DT method, we obtain the rational soliton solutions describing M-shaped soliton, W-shaped soliton, and the interactions on the plane wave and periodic background. The results can be useful to study the dynamical behaviors of soliton solutions in nonlocal wave models.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46315214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions Date–Jimbo–Kashiwara–Miwa方程的（2+1）维变系数扩展：李对称性分析、最优系统和精确解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-07 DOI: 10.1515/ijnsns-2021-0406
Yuru Hu, Feng Zhang, Xiangpeng Xin, Hanze Liu
{"title":"A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions","authors":"Yuru Hu, Feng Zhang, Xiangpeng Xin, Hanze Liu","doi":"10.1515/ijnsns-2021-0406","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0406","url":null,"abstract":"Abstract In this article, the Date–Jimbo–Kashiwara–Miwa equation is extended to a new variable-coefficients equation with respect to the time variable. The infinitesimal generators are acquired by studying the Lie symmetry analysis of the equation, and the optimal system of this equation is presented. After that, the equation performed similarity reductions, and the reduced partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) with the help of traveling wave transform. Then, the exact solutions are found by applying the extended tanh-function method. Finally, the structural features of exact solutions to different times are shown with the help of images.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44079661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems 研究非线性分式边值问题解存在性的一种新的广义方法
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-07-04 DOI: 10.1515/ijnsns-2021-0338
Asmat Batool, Imran Talib, Rym Bourguiba, I. Suwan, T. Abdeljawad, M. Riaz
{"title":"A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems","authors":"Asmat Batool, Imran Talib, Rym Bourguiba, I. Suwan, T. Abdeljawad, M. Riaz","doi":"10.1515/ijnsns-2021-0338","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0338","url":null,"abstract":"Abstract In this paper, we construct a new generalized result to study the existence of solutions of nonlinear fractional boundary value problems (FBVPs). The proposed results unify the existence criteria of certain FBVPs including periodic and antiperiodic as special cases that have been previously studied separately in the literature. The method we employ is topological in its nature and manifests themselves in the forms of differential inequalities (lower and upper solutions, and coupled lower and upper solutions (CLUSs)). Two examples are given to demonstrate the applicability of the developed theoretical results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43789032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The deterministic and stochastic solutions for the nonlinear Phi-4 equation 非线性pi -4方程的确定性和随机解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-06-16 DOI: 10.1515/ijnsns-2022-2272
M. Abdelrahman, M. Sohaly, S. Ammar, Yousef F. Alharbi
{"title":"The deterministic and stochastic solutions for the nonlinear Phi-4 equation","authors":"M. Abdelrahman, M. Sohaly, S. Ammar, Yousef F. Alharbi","doi":"10.1515/ijnsns-2022-2272","DOIUrl":"https://doi.org/10.1515/ijnsns-2022-2272","url":null,"abstract":"Abstract In the present work, the exp(−φ(ξ))-expansion method is applied for solving the deterministic and stochastic Phi-4 equation. Namely, we introduce hyperbolic, trigonometric, and rational function solutions. The computational study shows that the offered method is pretentious, robust, and influential in applications of interesting analysis, observations of particle physics, plasma physics, quantum field theory, and fluid dynamics. The control on the randomness input (the coefficients are random variables) is studied in order to obtain stability stochastic process solution with beta distribution. In this work, we will deal with stability moment method and then we apply the mean square calculus for the stability concept.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"23 1","pages":"823 - 832"},"PeriodicalIF":1.5,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44702830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The simulation of two-dimensional plane problems using ordinary state-based peridynamics 基于常态的周动力学模拟二维平面问题
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-06-13 DOI: 10.1515/ijnsns-2021-0320
Jingjing Zhao, Guangda Lu, Qing Zhang, W. Du
{"title":"The simulation of two-dimensional plane problems using ordinary state-based peridynamics","authors":"Jingjing Zhao, Guangda Lu, Qing Zhang, W. Du","doi":"10.1515/ijnsns-2021-0320","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0320","url":null,"abstract":"Abstract The ordinary state-based peridynamics (OSB PD) model is an integral nonlocal continuum mechanics model. And the three-dimensional OSB PD model can deal with linear elastic solid problems well. But for plane problems, the calculation results of existing models have large deviations. In this paper, a set of OSB PD models for plane problems is established by theoretical derivation. First, through the strain energy density function equivalence of peridynamics and classical continuum mechanics, the equivalent coefficients of the plane strain and plane stress problems of OSB PD are deduced. Then, consider the cantilever beam deformation simulation under concentrated load. The simulation results show that the maximum displacements are in good agreement with the corresponding analytical solutions in all directions. Finally, in the simulation of the slab with a hole, the two cases of uniform displacement and uniform load are considered, respectively. The simulation results are consistent with the ANSYS analysis results, and the deviation is small, which verifies the validity of the model.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48930661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Two new iterative schemes to approximate the fixed points for mappings 映射不动点逼近的两个新迭代方案
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-06-03 DOI: 10.1515/ijnsns-2021-0141
Aniruddha V. Deshmukh, D. Gopal, V. Rakočević
{"title":"Two new iterative schemes to approximate the fixed points for mappings","authors":"Aniruddha V. Deshmukh, D. Gopal, V. Rakočević","doi":"10.1515/ijnsns-2021-0141","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0141","url":null,"abstract":"Abstract In this article, we present a study of two iterative schemes to approximate the fixed points of enriched non-expansive maps and enriched generalized non-expansive maps. The schemes introduced in this article generalize those given by Thakur et al. in (“A new iterative scheme for approximating fixed points of nonexpansive mappings,” Filomat, vol. 30, no. 10, pp. 2711–2720, 2016.) and Ali et al. in (“Approximation of Fixed points for Suzuki’s generalized nonexpansive mappings,” Mathematics, vol. 7, no. 6, pp. 522–532, 2019.) in a sense that our schemes work for larger classes of enriched mappings and the schemes given by Thakur et al. and Ali et al. reduce to a particular case of our iterative techniques. Taking inspiration from Berinde (“Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators,” Fixed Point Theory Appl., vol. 2004, no. 2, pp. 97–105, 2004.) and Maniu (“On a three-step iteration process for Suzuki mappings with qualitative study,” Numer. Funct. Anal. Optim., 2020.), we also give stability results of the our procedures for enriched contractions (introduced by Berinde in 2019). Lastly, we compare the rate of convergence of our schemes with each other and the conventional Krasnoselskii iteration process used for approximating fixed points of enriched contractions along with some examples. As an application to the proposed iterative schemes, we give a few results on the solutions of linear system of equations.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"24 1","pages":"1265 - 1309"},"PeriodicalIF":1.5,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43434621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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