Laplace decomposition for solving nonlinear system of fractional order partial differential equations

Hassan Khan,Poom Kumam,Dumitru Baleanu,Muhammad Arif,Rasool Shah

doi:10.1186/s13662-020-02839-y

Abstract

In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.

Highlights

In the last decade, scientists and engineers have paid much attention towards nonlinear equations, as the nonlinearity exists everywhere in most of the physical problems
Many physical phenomena are dependent on time instant as well as at the earlier history of time are modeled by using fractional-order ordinary differential equations (FODEs), and FDEs have attained their importance in many fields of applied sciences
Laplace–Adomian decomposition method (LADM) possesses the combined behavior of Laplace transformation and Adomian decomposition method (ADM)

Summary

Introduction

Scientists and engineers have paid much attention towards nonlinear equations, as the nonlinearity exists everywhere in most of the physical problems. In this regard numerous techniques have been discussed for the solutions of FPDEs such as homotopy Exact solution of Kodomtsev–Petviashvili (KP) equation is obtained in [21] by using simple equation method. Modified variational iteration technique is developed in [2] for the result of nonlinear PDEs. The solution of linear and nonlinear FPDEs has been studied in [22] by using iterative Laplace transform method.

Results

Conclusion