A novel approach for the analytical solution of nonlinear time-fractional differential equations. Issue 4 (22nd July 2020)

• Record Type: Journal Article
• Authors: Zhang, Haiyan; Nadeem, Muhammad; Rauf, Asim; Guo Hui, Zhao
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 31:Issue 4(2021)
• Page Start: 1069
• Page End: 1084
• Publication Date: 2020-07-22
• Subjects: Caputo derivative -- Homotopy perturbation method -- Laplace transform -- Convergence -- Analytical solutions; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-02-2020-0077
• Languages: English
• ISSNs: 0961-5539

Abstract

Abstract : Purpose: The purpose of this paper is to suggest the solution of time-fractional Fornberg–Whitham and time-fractional Fokker–Planck equations by using a novel approach. Design/methodology/approach: First, some basic properties of fractional derivatives are defined to construct a novel approach. Second, modified Laplace homotopy perturbation method (HPM) is constructed which yields to a direct approach. Third, two numerical examples are presented to show the accuracy of this derived method and graphically results showed that this method is very effective. Finally, convergence of HPM is proved strictly with detail. Findings: It is not necessary to consider any type of assumptions and hypothesis for the development of this approach. Thus, the suggested method becomes very simple and a better approach for the solution of time-fractional differential equations. Originality/value: Although many analytical methods for the solution of fractional partial differential equations are presented in the literature. This novel approach demonstrates that the proposed approach can be applied directly without any kind of assumptions.