Differential Equations and Nonlinear Mechanics
Volume 2008 (2008), Article ID 686512, 16 pages
Research Article

Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method

O. Abdulaziz, I. Hashim, and A. Saif

Centre for Modelling and Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia

Received 12 August 2008; Accepted 30 October 2008

Academic Editor: Shijun Liao

Copyright © 2008 O. Abdulaziz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The homotopy analysis method (HAM) is applied to solve linear and nonlinear fractional partial differential equations (fPDEs). The fractional derivatives are described by Caputo's sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given. The test examples, which include a variable coefficient, inhomogeneous and hyperbolic-type equations, demonstrate the capability of HAM for nonlinear fPDEs.