Numerical and Analytical Solutions of Space-Time Fractional Partial Differential Equations by Using a New Double Integral Transform Method

Mohammed G. S. AL-Safi; Wurood R. Abd AL-Hussein; Rand Muhaned Fawzi

doi:10.24996/ijs.2023.64.4.31

Authors

Mohammed G. S. AL-Safi Department of Accounting- Al-Esraa University College, Baghdad, Iraq
Wurood R. Abd AL-Hussein Department of Accounting- Al-Esraa University College, Baghdad, Iraq
Rand Muhaned Fawzi Department of Accounting- Al-Esraa University College, Baghdad, Iraq https://orcid.org/0000-0003-0106-6688

DOI:

https://doi.org/10.24996/ijs.2023.64.4.31

Keywords:

Fractional Calculus, Caputo derivative, Fractional Partial, Differential Equations, Double Sumudu-Elzaki transform

Abstract

This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.