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Lie symmetry analysis to generalized fifth-order time-fractional KdV equation. (English) Zbl 1331.35025

Summary: In present paper, the generalized fifth-order time-fractional Korteweg-de Vries (KdV) equation and the particular time-fractional Kaup-Kupershmidt equation are considered, a systematic investigation to derive Lie point symmetries of the equations are presented and compared. Each of them has been transformed into a nonlinear ordinary differential equation with a new independent variable are investigated. The derivative corresponding to time-fractional in the reduced formula is known as the Erdélyi-Kober fractional derivative.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35K55 Nonlinear parabolic equations