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

TL;DR

This paper investigates space-time fractional telegraph equations with Hilfer, Hadamard, and Riesz-Feller derivatives, providing Fourier transforms of solutions and probabilistic interpretations for specific cases.

Contribution

It introduces solutions to fractional telegraph equations with mixed derivatives and offers Fourier transform formulas and probabilistic insights, advancing fractional differential equation analysis.

Findings

Fourier transforms of solutions derived

Probabilistic interpretations provided for specific cases

Enhanced understanding of fractional telegraph equations

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.