广义caputo型分数阶导数微分方程的同伦分析方法

IF 1.9 4区工程技术 Q3 ENGINEERING, MECHANICAL

Journal of Computational and Nonlinear Dynamics Pub Date : 2022-12-04 DOI:10.1115/1.4056392

Wafia Fafa, Z. Odibat, N. Shawagfeh

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引用次数: 1

摘要

本文对同伦分析方法进行了扩展和修正，以处理具有广义caputo型分数阶导数的微分方程。利用所提出的修正，成功地给出了这类模型的解析近似解。讨论了在使用分数阶算子时，该方法相对于辅助控制参数的有效收敛区域的确定。然后，主要通过举例验证了该方法的准确性和有效性，并与预测校正方法和RK4方法进行了比较。最后，期望所研究的广义算子及其方法能在分数阶微积分领域得到广泛应用。

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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The Homotopy Analysis Method for Solving Differential Equations with Generalized Caputo-Type Fractional Derivatives

This study expands and modifies the homotopy analysis method to handle differential equations with generalized Caputo-type fractional derivatives. Analytical approximate solutions for such models were successfully provided using the proposed modification. The determination of the valid region of convergence for the proposed method, with respect to the auxiliary control parameter, was discussed when using fractional operators. Then, mainly, the accuracy and effectiveness of the proposed method was verified through illustrative examples and comparisons with the predictor corrector method and RK4 method. Finally, it is expected that the studied generalized operators and the suggested method can be widely applied in the field of fractional calculus.

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来源期刊

Journal of Computational and Nonlinear Dynamics 工程技术-工程：机械

CiteScore

4.00

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.