On Distributed-Order Time-Fractional Telegraph Equations in Higher Dimensions

In this seminar, we study a class of distributed-order time-fractional telegraph equations in higher-dimensional spaces. Our main goal is to present the corresponding Cauchy problem and a representation of its fundamental solution, obtained by combining Fourier, Laplace, and Mellin transforms with the Fox H-function.
We then discuss some simple choices of the order distribution to illustrate the flexibility of the model. We also comment on the fractional moments of the fundamental solution. If time allows, we will briefly discuss the asymptotic behaviour of the second-order moment and its connection with Tauberian arguments.