A new fractional derivative for solving time fractional diffusion wave equation

Abstract

The time fractional diffusion wave equation, which can be used to describe wave diffusion process in this article, was studied. First of all, the diffusion wave equation can be extended to a generalized form in the sense of the regularized version of the ‐Hilfer–Prabhakar ( ‐H‐P) fractional operator involving the ‐Mittag‐ function. Then, the analytical solution can be obtained for this considered equation by using the Laplace transform method and the Fourier transform method. As a result, a novel and general solution have been found. The unconventional solution may show new result and phenomenon to wave diffusion process. Thereby, this research provides a window for discovering new diffusion mechanisms.