Analytical solution of the generalized space-time fractional ultra-hyperbolic differential equation

A generalization of the ultra-hyperbolic time-fractional diffusion-wave equation introduced by the author in Dorrego [The Mittag-Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation. Integral Transforms Spec. Funct. 2016;27(5):392-404] is presented and studied. The results obtained here extend the previous to the whole space R-n. The problem is solved by applying the integral transforms method and the analytical solution is given by the Fox H-function. Some interesting particular cases are analysed.