The new expansion method to solve Fractional KdV-Equations

TL;DR

This paper introduces a new expansion method for solving fractional KdV equations, utilizing fractional calculus of variation and providing more general solutions expressed through hyperbolic, trigonometric, and rational functions.

Contribution

It presents a novel expansion method for solving fractional KdV equations, enhancing solution generality compared to existing methods.

Findings

Solutions expressed in generalized hyperbolic, trigonometric, and rational functions.

Method yields more general solutions than previous approaches.

Applied to fractional KdV, demonstrating effectiveness.

Abstract

Fractional calculus of variation plays an important role to formulate the non-conservative physical problems. In this paper we use semi-inverse method and fractional variational principle to formulate the fractional order generalized Korteweg-deVries (KdV) equation with Jumarie type fractional derivative and proposed a new method to solve the non-linear fractional differential equation named as expansion method. Using this method we obtained the solutions of fractional order generalized KdV. The obtained solutions are more general compare to other method and the solutions are expressed in terms of the generalized hyperbolic, trigonometric functions and rational functions.