A comparative analytical investigation for some linear and nonlinear time-fractional partial differential equations in the framework of the Aboodh transformation

Abstract

This article discusses two simple, complication-free, and effective methods for solving fractional-order linear and nonlinear partial differential equations analytically: the Aboodh residual power series method (ARPSM) and the Aboodh transform iteration method (ATIM). The Caputo operator is utilized to define fractional order derivatives. In these methods, the analytical approximations are derived in series form. We calculate the first terms of the series and then estimate the absolute error resulting from leaving out the remaining terms to ensure the accuracy of the derived approximations and determine the accuracy and efficiency of the suggested methods. The derived approximations are discussed numerically using some values for the relevant parameters to the subject of the study. Useful examples are thought to illustrate the practical application of current approaches. We also examine the fractional order results that converge to the integer order solutions to ensure the accuracy of the derived approximations. Many researchers, particularly those in plasma physics, are anticipated to gain from modeling evolution equations describing nonlinear events in plasma systems.

Fractional dynamics study: analytical solutions of modified Kordeweg-de Vries equation and coupled Burger’s equations using Aboodh transform

“…The function is exponentially ordered and has piecewise continuity 72 . For , the Aboodh transform (AT) is defined as follows where : …”