Exact solitary wave solutions for a system of some nonlinear space–time fractional differential equations

Abstract

We have enumerated new and exact general wave solutions, along with multiple exact soliton solutions of space–time nonlinear fractional differential equations (FDE), namely Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM), foam drainage and symmetric regularised long-wave (SRLW) equations, by employing a relatively new technique called ( $$G^\prime /G, 1/G)$$ -expansion method. Also, based on fractional complex transformation and the properties of the modified Riemann–Liouville fractional-order operator, the fractional partial differential equations transform into a form of ordinary differential equation (ODE). This method is a recollection of the commutation of the well-appointed ( $$G^\prime /G$$ )-expansion method introduced by Wang et al, Phys. Lett. A 372, 417 (2008) In this paper, it is mentioned that the two-variable ( $$G^\prime /G, 1/G$$ )-expansion method is more legitimate, modest, sturdy and effective in the sense of theoretical and pragmatical point of view. Lastly, the peculiarities of these analytic solutions are illustrated graphically by utilising the computer symbolic programming Wolfram Mathematica.