www.astesj.com 8 Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (G ʹ /G)-Expansion Method Rashida Hussain, Tayyiaba Rasool * , Asghar Ali Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur-10250 (AJK), Pakistan. A R T I C L E I N F O A B S T R A C T Article history: Received: 09 March, 2017 Accepted: 29 March, 2017 Online: 07 April, 2017 In this paper, Novel (Gʹ/G)-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform. Keywords: Fractional complex transformation Fractional derivatives Fractional order coupled Burger’s equations Novel (Gʹ/G)-expansion method 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 ()+(. ) = ∇ 2 . 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 − 2 2 +2 + () = 0, − 2 2 +2 + () = 0, where 0< ≤ 1, 0 < ≤ 1, > 0. 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) + ( + 1) + ( + 1) + ( + 1) . 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]. ASTESJ ISSN: 2415-6698 * Coresponding: Tayyiaba Rasool, Mirpur University of Science and Technology Mirpur AJK, Pakistan, +923418903401, tayba481@yahoo.com Advances in Science, Technology and Engineering Systems Journal Vol. 2, No. 4, 8-13 (2017) www.astesj.com https://dx.doi.org/10.25046/aj020402