Novel Integral Transform Treating Some Ψ-Fractional Derivative Equations

Mourad Chamekh; Mohamed Ali Latrach; Tarig M. Elzaki

doi:10.2478/ama-2024-0060

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Novel Integral Transform Treating Some Ψ-Fractional Derivative Equations

Acta Mechanica et Automatica

Volume 18 (2024): Issue 3 (September 2024)

By: Mourad Chamekh , Mohamed Ali Latrach and Tarig M. Elzaki

Open Access

|Aug 2024

Abstract

The paper deals with a new integral transformation method called Ψ-Elzaki transform (PETM) in order to analyze some Ψ-fractional differential equations. The proposed method uses a modification of the Elzaki transform that is well adapted to deal with Ψ-fractional operators. To solve the nonlinear Ψ-fractional differential equations, we combine the PETM by an iterative method to overcome this nonlinearity. To validate the accuracy and efficiency of this approach, we compare the results of the discussed numerical examples with the exact solutions.

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Articles in this issue

DOI: https://doi.org/10.2478/ama-2024-0060 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

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Language: English

Page range: 571 - 578

Submitted on: Sep 25, 2023

Accepted on: Jan 21, 2024

Published on: Aug 1, 2024

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Ψ-Integral transform,

Ψ-Hilfer derivative,

Ψ-Caputo derivative,

Ψ-Hilfer fractional derivative equation

Related subjects:

Engineering,

Electrical engineering,

Electronics,

Mechanical engineering,

Mechanics,

Bioengineering and biomedical engineering,

Biomechanics,

Civil engineering,

Environmental engineering

© 2024 Mourad Chamekh, Mohamed Ali Latrach, Tarig M. Elzaki, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 18 (2024): Issue 3 (September 2024)