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

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