Distinct solutions of nonlinear space–time fractional evolution equations appearing in mathematical physics via a new technique

Abstract

Abstract In this paper, we furnished novel and different traveling wave solutions to the nonlinear space–time fractional Klein–Gordon (KG) equation and the nonlinear space–time fractional symmetric regularized long wave (SRLW) equation. The considered equations are turned into ordinary differential equations with the aid of fractional composite transformation in the sense of conformable fractional derivative and then the proposed improved tanh method along with Riccati equation is employed. Consequently, fresh and further general solutions in the shape of kink, bell, cuspon, compacton, periodic etc. are successfully obtained, which are compared with those in the literature. Further, it is important to point out that some of our solutions is in good harmony for a special case with already published results which in turn validates our other solutions. The comparison ensures the novelty of the proposed technique which might be taken into account for further research in future.