Analytical solution with tanh-method and fractional sub-equation method for non-linear partial differential equations and corresponding fractional differential equation composed with Jumarie fractional derivative

TL;DR

This paper introduces analytical solutions for non-linear differential equations and their fractional counterparts using tanh and fractional sub-equation methods, specifically with Jumarie fractional derivatives, providing novel solutions not previously reported.

Contribution

The paper applies tanh and fractional sub-equation methods to solve new classes of non-linear and fractional differential equations with Jumarie derivatives, yielding analytical traveling wave solutions.

Findings

Solutions obtained in analytical traveling wave form

First reported solutions for these specific equations

Demonstrates effectiveness of tanh and fractional sub-equation methods

Abstract

The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.