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Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative

Elkott Ibrahim, Abdel-Latif Mohamed S., El-Kalla Ibrahim L., Abdel Kader Abass H.

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 2

5--14

In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically.