Fractional telegraph equation, Mittag-Leffler function, Hilfer derivative, Hadamard fractional derivative, Riesz-Feller space-fractional derivative

Abstract

In this paper we consider space-time fractional telegraph equations, where the time derivatives are intended in the sense of Hilfer and Hadamard while the space fractional derivatives are meant in the sense of Riesz-Feller. We provide the Fourier transforms of the solutions of some Cauchy problems for these fractional equations. Probabilistic interpretations of some specific cases are also provided.