拉普拉斯-阿达姆分解法在三阶色散分数阶偏微分方程解析解中的应用

Application of Laplace-Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations.

作者信息

Shah Rasool, Khan Hassan, Arif Muhammad, Kumam Poom

机构信息

Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan.

Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.

出版信息

Entropy (Basel). 2019 Mar 28;21(4):335. doi: 10.3390/e21040335.

DOI:10.3390/e21040335

PMID:33267049

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7514819/

Abstract

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace-Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace-Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

摘要

在本文中，我们使用拉普拉斯 - 阿达马分解法求解分数阶色散偏微分方程的解析解。采用卡普托算子来定义分数阶导数。分别以级数形式得到了分数阶和整数阶的拉普拉斯 - 阿达马分解法解，表明所提方法具有较高的收敛性。通过实例验证了该方法的有效性。还研究了收敛于整数阶解的分数阶解。