1. Introduction

Fractional complex transformation as in [1] is utilized for transformation of nonlinear fractional order partial differential equations into nonlinear ordinary differential equations. The one-dimensional case of Burger’s equation was introduced by a Dutch scientist J. M. Burger in 1939 see [2], its general form is given as

Afterward, new type of Burger’s equation was presented in further research named as time-space fractional order coupled Burger’s equations [3], which has the form

where

     An assortment of approaches occurs for nonlinear equations which gives their travelling wave and numerical solutions. Wang et al. introduced (Gʹ/G)-expansion method [4]. This method was further reached out for coupled Burger’s equations by Younas et al. [3]. In this article Novel (Gʹ/G)-expansion method has been utilized to discover travelling wave solutions of nonlinear space and time fractional order coupled Burger’s equations.

1.1.  Fractional complex transformation

Fractional complex transform is the unobtrusive way for the transformation of the fractional order differential equation into integer order differential equation. This simplifies the rest of the procedure towards a solution. Presently consider

where L, M, N and O are constants.

     Let the fractional complex transformation in nonlinear fractional order coupled Burger’s equations be defined as

1.2.  Travelling wave solution

     Travelling wave solution was used for transformation of partial differential equations into ordinary differential equations. For this purpose, we consolidate two independent variables into one independent variable known as travelling wave variable x [5].

     Travelling wave solution of nonlinear partial differential equation

Conclusion

Novel (Gʹ/G)-expansion method is an effective method for finding exact solutions of the fractional order partial differential equation. As an application, exact solutions have been all around got for time-space fractional order coupled Burger’s equations. The fractional complex transformation used as a part of the exhibited work is very momentous. By utilizing this fractional transformation, fractional order partial differential equation can be converted into the integer order ordinary differential equation. Graphical portrayals insure that the required solutions are travelling wave solutions. Novel (Gʹ/G)-expansion method is an influential mathematical tool for solving the nonlinear partial differential equations.

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