Eur. Phys. J. Plus (2017) 132: 130
https://doi.org/10.1140/epjp/i2017-11407-y

Regular Article

A new optimization method for a class of time fractional convection-diffusion-wave equations with variable coefficients

Department of Mathematics, Shahrekord University, Shahrekord, Iran

^* e-mail: msh-dahaghin@sci.sku.ac.ir

Received: 20 November 2016
Accepted: 13 February 2017
Published online: 16 March 2017

Abstract

In this paper, we consider a class of time fractional convection-diffusion-wave equations (TFCDWE) with variable coefficients involving fractional derivatives in the Caputo sense. We also propose an optimization method based on the generalized polynomials (GPs) for solving TFCDWE. Our objective in the proposed method is to expand the solution of the problem under consideration in terms of GPs with unknown free coefficients and control parameters. Furthermore, we derive some operational matrices of the ordinary and fractional derivatives for these basis functions. Finally, we obtain the free coefficients and control parameters optimally by minimizing the error of the approximate solution. Some numerical examples are provided to demonstrate the validity and accuracy of the proposed method. The obtained results show that the proposed method is very efficient and accurate.