Fractional Analysis of Coupled Burgers Equations within Yang Caputo-Fabrizio Operator

Nehad Ali Shah,Essam R El-Zahar,Jae Dong Chung,Mahmut Isik

doi:10.1155/2022/6231921

Abstract

This work applies a novel analytical technique to the fractional view analysis of coupled Burgers equations. The proposed problems have been fractionally analyzed in the Caputo-Fabrizio sense. The Yang transformation was initially applied to the specified problem in the current approach. The series form solution is then obtained using the Adomian decomposition technique. The desired analytical solution is obtained after performing the inverse transform. Specific examples of fractional Burgers couple systems are used to validate the proposed technique. The current strategy has been found to be a useful methodology with a close match to actual solutions. The proposed method offers a lower computing cost and a faster convergence rate. As a result, the suggested technique can be applied to a variety of fractional order problems.

Highlights

The branch of mathematics, which deals with the study of derivatives and integrals of non-integer orders, is known as fractional calculus (FC)
FC has been used as a powerful tool by many researchers in various fields of science and engineering, for example, the fractional control theory [2, 5], anomalous diffusion, fractional neutron point kinetic model, fractional filters, soft matter mechanics, non-Fourier heat conduction, notably control theory, Levy statistics, nonlocal phenomena, fractional signal and image processing, porous media, fractional Brownian motion, relaxation, groundwater problems, rheology, acoustic dissipation, creep, fractional phase-locked loops, and fluid dynamics [6–10]
Yang Adomian decomposition method is implemented for the solution of dynamic systems of fractional Burger equations

Summary

Introduction

The branch of mathematics, which deals with the study of derivatives and integrals of non-integer orders, is known as fractional calculus (FC). The Burgers equation was initially introduced by Harry Bateman in the year 1915 [41] They have many applications in various fields, especially in equations having nonlinear form. Various techniques were developed by mathematicians to find the numerical and analytical solutions of Burgers equations. Some of these methods are a direct variational iteration method by Ozis and Ozdes [48]. Laplace Adomian decomposition method required less number of parameters, no discritization, and linerization as compared to other analytical technique. Laplace Adomian decomposition method is compared with ADM to analyze the solution of FPDEs given in [57]. The results have shown the present method has the desired accuracy as compared to other analytical techniques

Preliminary Concepts

Implementation of YDM with CaputoFabrizio

Example

Results and Discussion

Conclusion