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1 Journal of Applied Mathematics and Computational Mechanics

1 2024

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Inverse laplace transform for a new class of functions and its application to time-fractional diffusion-wave equations

Latif Mohamed S. Abdel, Elhadedy Hager, Kader Abass H. Abdel

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 4

56--65

This paper investigates the inverse Laplace transform of a certain class of functions. This inverse Laplace transform is obtained in the form of an infinite series of the three-parameter Mittag-Leffler function. Additionally, we found the sum of an infinite series of Mittag-Leffler functions with three parameters in terms of the Wright function. As an application, we get an exact solution of the time-fractional diffusion-wave equation with the Hilfer-Prabhakar time-fractional derivative using Laplace and Fourier transforms.