Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix

M. Basim, N. Senu, A. Ahmadian, Z. Ibrahim, S. Salahshour
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引用次数: 0

Abstract

This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems by reducing them to ones that can be solved by solving a set of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The suggested approaches are applied in solving non-linear and linear ABC problems according to initial conditions, and the efficiency and applicability of the proposed method are proved by several test examples. A lot of focus is placed on contrasting the numerical outcomes discovered by the new algorithm together with those discovered by previously well-known methods.
利用Jacobi运算矩阵求解非奇异导数的分数阶变阶微分方程
本研究导出了关于分数阶导数的移位Jacobi操作矩阵(JOM),并利用谱tau方法实现了Atangana-Baleanu Caputo (ABC)导数的数值解。这种方法的主要方面是,它通过将问题简化为可以通过求解一组代数方程来解决的问题,从而大大简化了问题。该方法的主要优点是鲁棒性和精度高,且使用的雅可比函数较少。将所提方法应用于求解非线性和线性ABC问题,并通过实例验证了所提方法的有效性和适用性。将新算法发现的数值结果与先前已知方法发现的结果进行比较是重点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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