A modified homotopy analysis method for solution of fractional wave equations. (5th December 2015)

• Record Type: Journal Article
• Authors: Yin, Xiang-Bao; Kumar, Sunil; Kumar, Devendra
• Is Part Of: Advances in mechanical engineering. Volume 7:Number 12(2015:Dec.)
• Publication Date: 2015-12-05
• Subjects: Fractional wave equation -- fractional derivatives -- analytical solution -- Mittag-Leffler function -- Laplace transform -- homotopy analysis transform method; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/1687814015620330
• Languages: English
• ISSNs: 1687-8132

Abstract

The aim of this article is to introduce a modified analytical approach to obtain quick and accurate solution of wave-like fractional physical models. This modified analytical approach is an innovative adjustment in Laplace transform algorithm and homotopy analysis method for fractional partial differential equations. The proposed technique solves the problems using Adomian's polynomials. The homotopy analysis transform method utilizes a simple and powerful method to adjust and control the convergence region of the infinite series solution using an auxiliary parameter. The numerical solutions obtained by this modified proposed method indicate that the approach is easy to implement, highly accurate, and computationally very attractive. A good agreement between the obtained solutions and some well-known results has been obtained.