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Advances in Mathematical Physics
Volume 2016, Article ID 7304659, 7 pages
http://dx.doi.org/10.1155/2016/7304659
Research Article

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

1Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt
2Mathematics & Engineering Physics Department, Faculty of Engineering, Modern University for Technology and Information, Cairo 11585, Egypt

Received 12 January 2016; Revised 19 March 2016; Accepted 29 March 2016

Academic Editor: Xiao-Jun Yang

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.

Abstract

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.