Abstract
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 . 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.
Acknowledgments
The author wishes to thank Dr R. Cerutti for the suggestions made on the possibility of defining the Mittag–Leffler type function (Equation3.5(3.5) (3.5) ).
Disclosure statement
No potential conflict of interest was reported by the author(s).