Stable numerical solutions of fractional partial differential equations using Legendre scaling functions operational matrix

Abstract

In this paper we solve initial and boundary value problem for non-homogeneous fractional order partial differential equations. Here we use operational matrix approach to construct approximate solutions using Legendre scaling functions as basis. We also give the error analysis of the proposed method. Some numerical examples are given to verify the theoretical bound of error and to show the stability of the proposed method. Results are also compared with some known methods and it is observed that our method is more easy to implement and accurate. 2016 Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).