Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations

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

doi:10.3390/app10020610

Abstract

In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations.

Highlights

Fractional calculus and fractional differential equations (FDEs) have attracted the attention of scientists, mathematicians and engineers
From the above properties of the present method, we expect that it can be modified for other fractional-order differential equations which arise in science and engineering
The fractional-order analysis of the acoustic wave equation is important to investigate the behaviour of the dynamics as compared to the classical one

Summary

Introduction

Fractional calculus and fractional differential equations (FDEs) have attracted the attention of scientists, mathematicians and engineers. A number of important implementations have been evaluated in various fields of sciences and engineering, such as material engineering, viscoelastic, electrochemistry, electromagnetic and dynamics physics which are described by fractional partial differential equations (FPDEs) [1]. There is no technique which provides an exact solution to the FDEs. Approximate approaches must be obtained by using techniques of series solution or linearization [2], followed by the application of proper numerical discretization [3,4,5] and system solvers [6,7,8]. Non-linear phenomena appear in a number of fields of engineering and sciences, such as solid state physics, chemical kinetics, non-linear spectroscopy, fluid physics, computational biology, quantum mechanics and thermodynamics etc. The concept of non-linearity is designed by various higher-order nonlinear partial differential equations (PDEs)

Methods

Results

Conclusion