Abstract
In this work we obtain the first and second fundamental solutions of the multidimensional time-fractional equation of order 2α, α ∈]0, 1], where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time.
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