Analysis of an axis-symmetric fractional diffusion-wave problem

Abstract

This paper presents an axis-symmetric fractional diffusion-wave problem which is considered in polar coordinates. The dynamic characteristics of the system are described with a partial fractional differential equation in terms of the Riemann-Liouville fractional derivative. This continuum problem is reduced to a countable infinite problem by using the method of separation of variables. In this way, the closed form solution of the problem is obtained. The Grunwald-Letnikov approach is applied to take a numerical evaluation. The compatibility and effectiveness of this approach are realized by some simulation results which are obtained by a MATLAB program. It can be seen that the analytical and numerical solutions overlap.