# Traveling Waves in Rational Expressions of Exponential Functions to the Conformable Time Fractional Jimbo-Miwa and Zakharov-Kuznetsov Equations

## TL;DR

This paper develops explicit rational solutions involving exponential functions for conformable time fractional Jimbo-Miwa and Zakharov-Kuznetsov equations using a generalized Kudryashov method and wave transformation.

## Contribution

It introduces a novel application of the Kudryashov method to conformable fractional PDEs, deriving explicit rational exponential solutions.

## Key findings

- Exact solutions expressed as rational functions of exponential expressions.
- Reduction of PDEs to ODEs via wave transformation.
- Explicit solutions demonstrate the method's effectiveness.

## Abstract

The conformable time fractional Jimbo-Miwa and Zakharov-Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one. The predicted solution is of the form of a rational expression of two finite series at both the numerator and the denominator. The terms of both series are of the powers of some functions having exponential expressions satisfying a particular ODE. The exact solutions are expressed explicitly in terms of powers of some exponential functions in form of rational expressions.