Abundant new exact solutions to the fractional nonlinear evolution equation via Riemann-Liouville derivative

Abstract

The space–time fractional equal width (EW) and the space–time fractional generalized equal width (GEW) equations are two important models that represent nonlinear dispersive waves, namely, waves ensuing in the shallow water channel, 1-D wave generation ascending in the nonlinear dispersive medium estimation, cold plasma hydro-magnetic waves, chemical kinematics, electromagnetic interaction, etc. In this article, we search advanced and broad-spectrum wave solutions of the formerly indicated models in diverse families in conjunction with the Riemann-Liouville fractional derivative via the double (G′/G,1/G)-expansion approach. The nonlinear fractional differential equations (NLFDEs) are transformed into ODEs by the composite function derivative and the chain rule putting together with the wave transformation. We acquire kink wave solution, multiple periodic solutions, single soliton solution, periodic wave solution and other types of soliton solutions by setting particular values of the embodied parameters. The suggested technique is functional, convenient, powerful, and computationally feasible to examine scores of NLFDEs.

Keywords

• Solitary wave
• Riemann-Liouville fractional derivative
• Nonlinear fractional differential equation
• Wave transformation
• Double(G'/G,1/G)-expansion method