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2 Journal of Applied Mathematics and Computational Mechanics

2 2024

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The velocity field to unsteady fluid flow in a circular cylinder with generalized caputo fractional derivative

Eman Mohamed M., Kader Abass H. Abdel

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 4

66--75

In this paper, we study the velocity field corresponding to the unsteady flow of a second-grade fluid with a generalized Caputo fractional derivative in a circular cylinder. The analytical solution of the velocity field has been obtained utilizing the Laplace and the finite Hankel transforms. The solution is obtained in terms of a series containing the Mittag-Leffler functions, being the generalization of the exponential function. The effect of the fractional parameters and on fluid motion are illustrated graphically for three different cases. The model discussed in this work is more general and can be applied to other fluid models.

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.