Numerical treatment of some fractional nonlinear equations by Elzaki transform

Abstract

This study solves systems of partial differential equations with fractional-order derivatives using a modified decomposition approach. Fractional-order derivatives are expressed using the Caputo operator. The validity of the suggested technique is tested using illustrative cases. The exact and Elzaki Adomian decomposition method (EADM) solutions were in close proximity, according to the solution graphs. The suggested strategy’s dependability is shown by the fact that fractional-order problems tend to converge on the solution to an integer-order problem. The present approach may be utilized to answer a broad variety of fractional-order issues since it is more precise and simple to use. Finally, some examples show how the new strategy is uncomplicated, effective, and precise. The approximate solutions have also been displayed at the conclusion of this study.