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

Authors: DOĞAN KAYA, GULISTAN ISKANDAROVA

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

Keywords: Lie groups method, conservation laws, generalized KdV equation, Riemann-Liouville derivative

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