Fractional diffusion-wave equations on finite interval by Laplace transform

Abstract

In this work the solution of the fractional diffusion-wave equation on the finite interval [0, 1] with inhomogeneous boundary conditions is considered by the Laplace transform and the contour integration method. For the fractional diffusion equation the solution is expressed as an infinite integral, and for the fractional wave equation the solution is expressed as a sum of an infinite integral and a series. Finally, we compare the results with that by the method of separation of variables.