Fundamental solution of the multi-dimensional time fractional telegraph equation

What is it about?

The telegraphic equation is a generalization of the diffusion and wave equations due to the simultaneous presence of first and second order time derivatives, allowing to describe both diffusive and wave- like phenomena. Its fractional version gives us the possibility of describing memory and heredity properties of telegraph processes. We obtain integral and series representation of the fundamental solution (FS) of the multidimensional time-fractional telegraph equation where the time-fractional derivatives of orders α ∈]0,1] and β ∈]1,2] are in the Caputo sense. The fundamental solution allows solving other Cauchy type problems.

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Why is it important?

The work studies the telegraphic equation in higher dimensions and shows that the fundamental solution has a different series representation depending on the parity of the dimension.