Mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation with \( \alpha \in (0,2) \)
Using the properties of the Mittag-Leffler and the Mainardi functions together with the method of separation of variables, the authors obtain new expression for the solutions of a Cauchy problem of the time-fractional diffusion-wave equation in the upper half-plane, \(x\in \mathbb {R}\), \(t\in \mathbb {R}^+\), where the Caputo fractional derivative of order \(\alpha \in (0,2) \) is considered. Several new properties of the solution, using the stated expression, are presented.
scientific article; zbMATH DE number 6864556
scientific article