NUMERICAL ANALYSIS OF COUPLED FRACTIONAL DIFFERENTIAL EQUATIONS WITH ATANGANA-BALEANU FRACTIONAL DERIVATIVE

ILKNUR KOCA

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NUMERICAL ANALYSIS OF COUPLED FRACTIONAL DIFFERENTIAL EQUATIONS WITH ATANGANA-BALEANU FRACTIONAL DERIVATIVE

机译：atangana-Balanu分数衍生物耦合分数微分方程的数值分析

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摘要

A nonlinear system of two fractional nonlinear differential equa-tions with Atangana-Baleanu derivative is considered in this work. General conditions under which a system solution exists and unique are presented us-ing the fixed-point theorem method. The well-established numerical scheme is used to solve the system of equations. A numerical analysis is presented to secure the stability and convergence of the used numerical scheme.

机译：在这项工作中考虑了具有Atangana-Balanu衍生物的两个分数非线性微分方式的非线性系统。展示了系统解决方案的一般条件，并呈现了固定点定理方法。良好的现实数字方案用于解决方程系统。提出了数值分析以确保使用的数值方案的稳定性和收敛性。

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《Discrete and continuous dynamical systems▼hSeries S》 |2019年第3期|475-486|共12页
作者
ILKNUR KOCA;
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作者单位

Mehmet Akif Ersoy University Department of Mathematics Faculty of Sciences 15100 Burdur Turkey;

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正文语种 eng
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关键词
Non-linear equations; existence and uniqueness; Atangana-Baleanu fractional differentiation; numerical analysis;

机译：非线性方程;存在和唯一性;Atangana-Balanu分数分解;数值分析;

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1. Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods [J] . Saad K. M., Khader M. M., Gomez-Aguilar J. F., Chaos . 2019,第1a3期

机译：使用光谱搭配方法与Atangana-Balanu分数衍生物分数渔业型方程的数值解
2. On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach [J] . Allahviranloo Tofigh, Ghanbari Behzad Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2020,第期

机译：atangana-baleanu分数衍生方法的模糊分数微分方程
3. 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。
4. The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives [C] . Arman Dabiri, Laya Karimi Annual American Control Conference . 2019

机译：Riemann-Liouville导数分数阶微分方程数值解的分数切比雪夫搭配方法
5. Fractional derivatives, fractional differential equations, and their numerical approximation [D] . Hatcher, Christopher 2013

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6. Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations [O] . Fukang Yin, Junqiang Song, Hongze Leng, -1

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7. A New Coupled Fractional Reduced Differential Transform Method for the Numerical Solutions of(2+1)-Dimensional Time Fractional Coupled Burger Equations [O] . S. Saha Ray 2014

机译：一种新的（2 + 1） - 二维时间分数耦合汉堡方程数值解的新耦合分数减小差分变换方法

NUMERICAL ANALYSIS OF COUPLED FRACTIONAL DIFFERENTIAL EQUATIONS WITH ATANGANA-BALEANU FRACTIONAL DERIVATIVE

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