Fractional diffusion-wave problem in cylindrical coordinates

In this Letter, we present analytical and numerical solutions for an axis-symmetric diffusion-wave equation. For problem formulation, the fractional time derivative is described in the sense of Riemann–Liouville. The analytical solution of the problem is determined by using the method of separation of variables. Eigenfunctions whose linear combination constitute the closed form of the solution are obtained. For numerical computation, the fractional derivative is approximated using the Grünwald–Letnikov scheme. Simulation results are given for different values of order of fractional derivative. We indicate the effectiveness of numerical scheme by comparing the numerical and the analytical results for α=1α=1 which represents the order of derivative.