Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives

Liu Xiping; Jia Mei

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Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives

机译：涉及左右分数衍生物的分数耦合系统的BVPS的可解性和数值模拟

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We study the three-point boundary value problems for the fractional differential coupled systems with both left and right fractional derivatives in the paper. Firstly, the upper-lower solutions method for the systems is presented and some existence results to the systems solutions are also obtained. Secondly, we also give out an iterative approach for finding approximate solutions of the systems. Finally, we consider a concrete example where we obtain the existence result of the solution and also give out its numerical solution and the graphical simulation. (C) 2019 Elsevier Inc. All rights reserved.

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来源
《Applied mathematics and computation》 |2019年第2019期|共13页
作者
Liu Xiping; Jia Mei;
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作者单位

Univ Shanghai Sci &

Technol Coll Sci Shanghai 200093 Peoples R China;

Univ Shanghai Sci &

Technol Coll Sci Shanghai 200093 Peoples R China;

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正文语种 eng
中图分类数值分析;
关键词
Fractional coupled systems; Left and right fractional derivatives; Boundary value problems; Upper-lower solutions method; Iterative approach; Numerical solution;

机译：分数耦合系统;左右分数衍生物;边值问题;上下解法方法;迭代方法;数值解决方案;

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专利

1. Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives [J] . Liu Xiping, Jia Mei Applied mathematics and computation . 2019,第期

机译：涉及左右分数衍生物的分数耦合系统的BVPS的可解性和数值模拟
2. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
3. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential [J] . Kaihong Zhao, Ping Gong Mathematica Slovaca . 2017,第2期

机译：非局部积分BVP的正解，涉及高阶分数差分的非线性耦合系统
4. Computational Simulations for Solving a Class of Fractional Models via Caputo-Fabrizio Fractional Derivative [C] . A.S.V. Ravi Kanth, Neetu Garg International Conference on Smart Computing and Communications . 2018

机译：通过Caputo-Fabrizio分数衍生物解决一类分数模型的计算模拟
5. Fractional derivatives, fractional differential equations, and their numerical approximation [D] . Hatcher, Christopher 2013

机译：分数阶导数，分数阶微分方程及其数值逼近
6. An Efficient Method for Systems of Variable Coefficient Coupled Burgers Equation with Time-Fractional Derivative [O] . Hossein Aminikhah, Nasrin Malekzadeh 2013

机译：具有时间分数阶导数的变系数Burgers方程组的一种有效方法
7. Existence of solutions of BVPs for impulsive fractional Langevin equations involving Caputo fractional derivatives [O] . Yuji LIU, Ravi AGARWAL 2019

机译：涉及Caputo分数衍生物的冲动分数Langevin方程的BVPS解决方案

Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives

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