Traveling Wave Solutions to Conformable Time Fractional RLW-class equations

TL;DR

This paper derives explicit traveling wave solutions for conformable time fractional RLW-class equations using sech and csch ansatzes, transforming PDEs into ODEs and solving for specific solution forms.

Contribution

It introduces a method to obtain explicit solutions for conformable time fractional RLW equations using ansatz-based transformations.

Findings

Explicit solutions expressed in terms of sech and csch functions.

Transformation of fractional PDEs into ODEs simplifies solution process.

Parameter relations among solutions are explicitly determined.

Abstract

The traveling wave solutions to some nonlinear conformable time fractional partial differential equations in RLW-class are set up by using sech and csch ansatzs. The conformable time fractional forms of the equal-width (EW), regularized long wave (RLW) and symmetric regularized long wave (sRLW) equations are considered in the study. By the assist of the simple traveling wave transformation, the equations are converted to some ordinary differential equations. Then, assuming these equations have solutions of forms of powers of sech and csch functions lead to determine the powers of the solutions if exist. The determination of the relation among the other parameters in the solutions follows the previous process. Finally, the solutions are expressed in some explicit forms.