Comparative Analytical study of Fractional Differential Equations via Abaaub - Shkheam, Mellim, and Laplace Transforms - Marwah .A. Aldhabaa (Journal of Scientific and Human Dimensions, 2026)
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.