Homotopy analysis method for space‐time fractional differential equations
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 2 August 2013
Abstract
Purpose
In this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial conditions.
Design/methodology/approach
The series solution is developed and the recurrence relations are given explicitly. The initial approximation can be determined by imposing the initial conditions.
Findings
The comparison of the HAM results with the exact solutions is made; the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter h, which provides a simple way to adjust and control the convergence region of series solution. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter h on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders a and b on the solution behavior.
Originality/value
The idea can be used to find the numerical solutions of other fractional differential equations.
Keywords
Citation
Zhang, X., Wei, L., Tang, B. and He, Y. (2013), "Homotopy analysis method for space‐time fractional differential equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 6, pp. 1063-1075. https://doi.org/10.1108/HFF-09-2011-0181
Publisher
:Emerald Group Publishing Limited
Copyright © 2013, Emerald Group Publishing Limited