Analytical solutions of nonlinear time fractional evaluation equations via unified method with different derivatives and their comparison

Abstract

This paper is devoted to addressings the fairly interesting soliton solutions for the time fractional combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV–mKdV equation) and modified Burgers-KdV equation. The unified method along with conformable, Beta and local M-derivative are used to construct the general structure of solitary wave soliton solutions. The method allows us to find solutions in both polynomial and rational forms. Further, the comparison of solutions are given out through 3D and 2D-plots to expose the impact of fractional parameter on the obtained solutions. The reported solutions are novel and have not been discussed in the literature.

Keywords

• Conformable
• Beta and local M-derivative
• The unified method
• Combined KdV-mKdV equation
• Modified Burgers-KdV equation
• Solitary wave soliton solutions