On finite series solutions of conformable time-fractional Cahn-Allen equation

Hadi Rezazadeh,Asim Zafar,Khalid K Ali

doi:10.1515/nleng-2020-0008

Abstract

AbstractThe aim of this article is to derive new exact solutions of conformable time-fractional Cahn-Allen equation. We have achieved this aim by hyperbolic function and expa function methods with the aid of symbolic computation using Mathematica. This idea seems to be very easy to employ with reliable results. The time fractional Cahn-Allen equation is reduced to respective nonlinear ordinary differential equation of fractional order. Also, we have depicted graphically the constructed solutions.

Highlights

Fractional differential equation may be considered as the missing part of the classical differential equations
Many authors have studied the nonlinear fractional differential equations for example see [1,2,3,4,5,6,7,8] because these equations express many complex nonlinear physical phenomena and dynamic forms in physics
Several definitions of fractional derivative have been presented to the literature, amongst are Atangana Baleanu operator, CaputoFabrizio and conformable derivative

Summary

Introduction

Fractional differential equation may be considered as the missing part of the classical differential equations. We apply two methods on conformable time-fractional Cahn-Allen equation to scrutinize the new explicit exact solutions [9,10,11,12] that may read as. A. Zafar et al, On finite series solutions of conformable time-fractional Cahn-Allen equation. The present subsection provides a brief explanation for two reliable techniques in engendering new exact solutions to nonlinear conformable time-fractional equation. For this purpose, suppose that we have a nonlinear conformable time FDE that can be presented in the form. = sinh(ρ), we find sinh(ρ) = ±csch(η), cosh(ρ) = − coth(η) and sinh(ρ) = ±ısech(η), cosh(ρ) =.

The exp a function approach

The hyperbolic function approach

Conclusion