Closed-form travelling wave solutions to the nonlinear space-time fractional coupled Burgers’ equation

Abstract

Fractional order nonlinear evolution equations play important roles to give a depiction of the complex physical phenomena of real world. The main aim of this article is to extract exact analytic solutions to the space-time fractional coupled Burgers' equation in the sense of conformable fractional derivative. A suitable composite transformation is implemented to reduce the considered equation into an ordinary differential equation of fractional order. Then a new approach, called the rational fractional ðD a n G=GÞ-expansion method, the Exp-function method and the extended tanh method, is employed to construct the closed-form solutions. This effort makes available the travelling wave solutions in terms of hyperbolic function, trigonometric function and rational function, which are found to be newer and more general than the existing results in the literature. The proposed method is highly efficient and may further be used to invstigate entirely new solutions to many other fractional evolution equations.

Application of the rational (G' /G)-expansion method for solving some coupled and combined wave equations

“…The NLPDEs have interesting structures that deals with many phenomena in physics, chemistry and engineering, for example; in fluid flow, plasma waves, mechanics, solid state physics, oceanic phenomena, atmospheric phenomena and so on. Many researchers have been proposed various different methods to find solutions for nonlinear partial differential equations and nonlinear fractional differential equations [36][37][38][39][40]. Such as the inverse scattering transform method [1], the Hirota's bilinear method [2], truncated Painlevé expansion method [3], the tanh-function expansion method [4], the Jacobi elliptic function expansion method [5], the homogeneous balance method [6][7][8], the trial function method [9], the exp-function method [10,34], differential transform method [33], the Bäcklund transform method [11], the generalized Riccati equation method [12][13][14][15], the sub-ODE method [17][18][19][20], the original (G ′ /G)-expansion method [16,29], the double (G ′ /G,1/G)-expansion method [35] etc..…”

Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics

“…In this study, we offer a newly established technique, called the rational fractional ðD α ξ G=GÞ-expansion method [42], to investigate closed form analytic wave solutions to some FNLEEs in the sense of conformable fractional derivative [43]. This effectual and reliable productive method shows its high performance through providing abundant fresh and general solutions to the suggested equations.…”

Spectrally accurate approximate solutions and convergence analysis of fractional Burgers’ equation

“…Cenesiz et al [7] have obtained new type exact solutions for time-fractional Burgers' equation, modified Burgers' equation, and Burgers'-Korteweg-de-Vries equation using first integral method. Islam et al [15] have obtained extract exact solutions for space-time-fractional Burgers' equation using rational fractional expansion method. Furthermore, authors have also employed expfunction method and the extended tanh method to construct the closed form solutions.…”