Solution of the KdV equation with fractional time derivative via variational method

Abstract

This article presents a formulation of the time-fractional generalized Korteweg-de Vries (KdV) equation using the Euler-Lagrange variational technique in the Riemann-Liouville derivative sense. It finds an approximate solitary wave solution, and shows that He's variational iteration method is an efficient technique in finding the solution.

Keywords

• Riemann-Liouville fractional derivative
• Euler-Lagrange equation
• Riesz fractional derivative
• generalized KdV equation
• He's variational iteration method
• solitary wave