Comparative Analytical study of Fractional Differential Equations via Abaaub - Shkheam, Mellim, and Laplace Transforms

Authors

  • Marwah .A. Aldhabaa General Department. The Higher Institute of Science and Technology in Al-Asabaa, Al-Asabaa, Libya Author

DOI:

https://doi.org/10.65421/jshd.v2i2.149

Keywords:

Fractional Differential Equations, Comparative Analysis, Laplace Transform, Mellin Transform Abaoub–Shkheam Transform, Analytical Methods, Integral Transforms Fractional Calculus, Exact Solutions

Abstract

The Paper presents a rigorous comparator analysis of fractional differential equation  F(t) of order α =  1/2  . We investigate the analytical solutions obtained through the modern Abaoub - Shkheam Transform, the complex - domain Mellin Transform, and the classical Laplace Transform. The study demonstrates that while the methodologies differ in their operational domains, they converge to a unique solution involving the Mittay-leffler function. The efficiency and parametric flexibility of the Abaoub-Shkheam Transform are highlighted.

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Published

2026-04-23

Issue

Volume 2, Issue 2, 2026

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Comparative Analytical study of Fractional Differential Equations via Abaaub - Shkheam, Mellim, and Laplace Transforms. (2026). Journal of Scientific and Human Dimensions, 2(2), 163-168. https://doi.org/10.65421/jshd.v2i2.149