Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation

TL;DR

This paper derives exact solutions for classical and fractional KP-Burger and coupled KdV equations using generalized Tanh and fractional sub-equation methods, demonstrating how solutions transition to classical forms as fractional order approaches one.

Contribution

It introduces the application of generalized Tanh and fractional sub-equation methods to obtain analytical solutions for fractional and classical KP-Burger and coupled KdV equations, highlighting the transition of solutions.

Findings

Solutions reduce to shock and soliton forms as fractional order approaches one.

Exact solutions are obtained for both classical and fractional equations.

Numerical simulations confirm the analytical results.

Abstract

Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by fractional sub-equation method reduces to classical solution when order of fractional derivative tends to one. Finally numerical simulation has done. The numerical simulation justifies that the solutions of two fractional differential equations reduces to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when order of derivative tends to one.