Exact wave solutions for the nonlinear time fractional Sharma–Tasso–Olver equation and the fractional Klein–Gordon equation in mathematical physics

Abstract

In this study, we examine the resourceful traveling wave solutions of a pair of nonlinear time fractional differential equations, namely, the general time fractional Sharma–Tasso–Olver equation and the fractional Klein–Gordon equation in the form of hyperbolic functions, trigonometric functions, and rational functions along with free parameters. To establish above mentioned type of solutions those are factual, convenient to use and penetrate the fission and fusion phenomena take place in solitons, the relativistic energy–momentum relation, scalar electrodynamics, electromagnetic interactions, plasma physics, nuclear physics etc. very clearly, we implement the new generalized $$\left( {G'/G} \right)$$ -expansion method. We emphasize that this method is highly effective and a forcible mathematical tool to extract solitary wave solutions of the time fractional models that are extensively used in theoretical physics.