Mathematical Analysis of a Cauchy Problem for the Time-Fractional Diffusion-Wave Equation with alpha is an element of (0,2)

摘要

This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, , , where the Caputo fractional derivative of order is considered. An explicit solution to this Cauchy problem is obtained via separation of variables. A first proof of the validity of the obtained results is provided for a certain kind of initial conditions. Throughout this work a new expression of the solution to this problem and its utility for carrying out rigurous proofs are presented. Finally, several new properties of the solution are obtained.