Application of New Iterative Method to Time Fractional Whitham–Broer–Kaup Equations

Rashid Nawaz,Meshal Shutaywi,Zahir Shah,Wejdan Deebani,Samreen Farid,Poom Kumam

doi:10.3389/fphy.2020.00104

Abstract

This article presents the Fractional Laplace transform with the help of new iterative method for finding the approximate solutions of coupled system of fractional order partial differential equations. The time fractional Whitham-Broer-Kaup system is taken as test example The fractional derivatives are described in the Caputo sense. Numerical results obtained by the proposed method are compared with that of Adomian Decomposition Method (ADM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic Method (OHAM).Numerical results show that the proposed method is reliable and efficient for solution of fractional order coupled system partial differential equations. The accuracy of the method increases by taking higher order approximations.

Highlights

As we know that many technical and engineering issues that arises in day-by-day existence are modeled via mathematical tools form fractional calculus (FC), i.e., fractional calculus can be used to simulate various real phenomena involving long memory, e.g., using fractional derivative, one can model HIV/AIDS model based on the effect of screening of unaware infectives [1]
new iterative method (NIM) was introduced by Daftardar-Gejji and Jafari in 2006 and is known as the DJ method for the solution of non-linear equations
We have extended the applications of the DJ method to a solution of coupled WBK equations of fractional order using the fractional Laplace Transform

Summary

INTRODUCTION

As we know that many technical and engineering issues that arises in day-by-day existence are modeled via mathematical tools form fractional calculus (FC), i.e., fractional calculus can be used to simulate various real phenomena involving long memory, e.g., using fractional derivative, one can model HIV/AIDS model based on the effect of screening of unaware infectives [1]. Maximum problems that arise are non-linear, and it is not usually probable to locate systematic results of such problems since some researchers introduced new approaches for finding the exact solution of FPDEs [2] These methods have some drawbacks, and we cannot use it for any type of problems. NIM was introduced by Daftardar-Gejji and Jafari in 2006 and is known as the DJ method for the solution of non-linear equations. We have no need to compute tedious Adomian’s polynomial in each iteration In this presentation, we have extended the applications of the DJ method to a solution of coupled WBK equations of fractional order using the fractional Laplace Transform. Values of the parameters are taken to be same as problem 3.1

AND DISCUSSION

CONCLUSION

DATA AVAILABILITY STATEMENT