The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

Abstract

This work studies two important temporal fractional nonlinear evolution equations, namely the (2+1)-dimensional Chaffee–Infante equation and (1+1)-dimensional Zakharov equation by way of the unified method along with properties of local M-derivative. The typical structures of fractional optical soliton wave solutions are obtained in polynomial and rational forms. Further, to grant the validity of non-singular solutions are given with limitation conditions and graphically depicted in 3D. Also, to expose the effect of a local fractional parameter on expected non-singular solutions are depicted through 2D graphs. The predicted solutions are revealing that the proposed approach is straightforward and valuable to find the solitary wave solutions of other nonlinear evolution equations.

Keywords

• Local M-derivative
• The unified method
• Chaffee–Infante equation
• Zakharov equation
• Optical fractional solitons