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International Journal of Differential Equations
Volume 2016 (2016), Article ID 2371837, 9 pages
Research Article

Semianalytic Solution of Space-Time Fractional Diffusion Equation

Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt

Received 30 April 2016; Accepted 3 July 2016

Academic Editor: Elena Kaikina

Copyright © 2016 A. Elsaid 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.


We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.