A New Numerical Technique For Solving Fractional Partial Differential Equations

TL;DR

This paper introduces the conformable Adomian decomposition method (CADM) for solving fractional partial differential equations, providing an efficient alternative to existing methods like CRDTM with convergent series solutions.

Contribution

The paper presents a novel CADM based on conformable derivatives for FPDEs and compares its effectiveness with the existing CRDTM method.

Findings

CADM produces easy, fast, and reliable solutions for FPDEs.

Numerical results show CADM's solutions are comparable to exact solutions.

The method is applicable to both linear and nonlinear problems.

Abstract

We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the same time, conformable reduced differential transform method (CRDTM) for FPDEs is briely given and a numerical comparison is made between this method and the newly introduced CADM. In applied science, CADM can be used as an alternative method to obtain approximate and analytical solutions for FPDEs as CRDTM. In this study, linear and non-linear three problems are solved by these two methods. In these methods, the obtained solutions take the form of a convergent series with easily computable algorithms. For the applications, the obtained results by these methods are compared to each other and with the exact solutions. When applied to FPDEs, it is seem that CADM approach produces easy, fast and reliable solutions as CRDTM.