ANALYTIC SOLUTION FOR THE TIME-FRACTIONAL TELEGRAPH EQUATION DEFINED IN A BOUNDED DOMAIN

In this paper, we discuss the so-called time-fractional telegraph equation. It is a generalization of the classical telegraph equation in case the first- and two-order time derivatives are replaced with Caputo derivatives of order $\alpha\in(\frac{1}{2},1], 2\alpha\in(1,2]$. By using the spatial finite sine and cosine transform, and the temporal Laplace transform, the existence of the analytic solutions of its initial-boundary problems in a boundedspace domain with Dirichlet and Neumann boundary conditions is derived. The analytic solutions are given in the form of series of the Mittag-Leffler functions.