Lie group analysis for initial and boundary value problem of time-fractional nonlinear generalized KdV partial differential equation

Abstract

The Lie group analysis or in other word the symmetry analysis method is extended to deal with a timefractionalorder derivative nonlinear generalized KdV equation. Our research in this work aims to use transformationmethods and their analysis to search for exact solutions to the nonlinear generalized KdV differential equation. It is shownthat this equation can be reduced to an equation with Erdelyi–Kober fractional derivative. In this study, we research theinitial and boundary conditions, considering them invariant, and so we get two ordinary initial value problems, i.e. twoCauchy problems. Conservation laws for the given equation are also investigated. In this work, we introduce symmetryanalysis and find conservation laws for the nonlinear generalized time-fractional KdV equation by the Lie groups methodusing fractional derivatives in the Riemann–Liouville sense.