A new approach to study nonlinear space-time fractional sine-Gordon and Burgers equations

Abstract

In this study, we investigate a couple of nonlinear fractional differential equations namely, the sine-Gordon and Burgers equations in the sense of Riemann-Liouville fractional derivative. In order to examine exact solutions effectively applicable in relaxation and diffusion problems, crystal defects, solid-state physics, plasma physics, vibration theory, astrophysical fusion plasmas, scalar electrodynamics, etc. we introduce the new generalized -expansion method. The method is highly effective and a functional mathematical scheme to examine solitary wave solutions to diverse fractional physical models.