A computational method for solving variable-order fractional nonlinear diffusion-wave equation

Abstract

In this paper, we generalize a one-dimensional fractional diffusion-wave equation to a one-dimensional variable-order space-time fractional nonlinear diffusion-wave equation (V-OS-TFND-WE) where the variable-order fractional derivatives are considered in the Caputo type. To solve this introduced equation, an easy-to-follow method is proposed which is based on the Chebyshev cardinal functions coupling with the tau and collocation methods. To carry out the method, an operational matrix of variable-order fractional derivative (OMV-OFD) is derived for the Chebyshev cardinal functions to be employed for expanding the unknown function. The proposed method can provide highly accurate approximate solutions by reducing the problem under study to a system of nonlinear algebraic equations which is technically simpler for handling. The experimental results confirm the applicability and effectiveness of the method.