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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.

The distinguishing features of the fundamental solution to the diffusion-wave equation

Povstenko J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 2

63-70

The time-fractional diffusion-wave equation with the Caputo derivative is considered. The typical features of the solution to the Cauchy problem for this equation are discussed depending on values of the order of fractional derivative.