Exact Solution of Two-Dimensional Fractional Partial Differential Equations

Dumitru Baleanu,Hassan Kamil Jassim

doi:10.3390/fractalfract4020021

Dumitru Baleanu, Hassan Kamil Jassim

Open Access

https://doi.org/10.3390/fractalfract4020021

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Journal: Fractal and Fractional	Publication Date: May 12, 2020
Citations: 25	License type: CC BY 4.0

Affiliation: Çankaya University, Thi Qar University

Abstract

In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.

Highlights

Fractional calculus has been utilized as an excellent instrument to discover the hidden aspects of various material and physical processes that deal with derivatives and integrals of arbitrary orders [1,2,3,4]
We stress on the fact than by replacing the classical derivative with respect with time by a given fractional operator we change the nature of the partial differential equation from local to a nonlocal one
The fractional Sumudu decomposition method (FSDM) is a graceful coupling of two powerful techniques, namely Adomian decomposition method (ADM) and Sumudu transform algorithms and gives more refined convergent series solution

Summary

Introduction

Fractional calculus has been utilized as an excellent instrument to discover the hidden aspects of various material and physical processes that deal with derivatives and integrals of arbitrary orders [1,2,3,4]. Varieties of them play important roles and tools, in mathematics, and in physics, dynamical systems, control systems and engineering, to create the mathematical modeling of many physical phenomena. We stress on the fact than by replacing the classical derivative with respect with time by a given fractional operator we change the nature of the partial differential equation from local to a nonlocal one. In this way we can describe better processes with faster of lower velocities, depending on the value of alpha, which in the classical class we cannot do. The FSDM is a graceful coupling of two powerful techniques, namely ADM and Sumudu transform algorithms and gives more refined convergent series solution

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