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Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations. (English) Zbl 1245.35142
Summary: A systematic investigation to derive Lie point symmetries to time fractional generalized Burgers as well as Korteweg-de Vries equations is presented. Using the obtained Lie point symmetries we have shown that each of them has been transformed into a nonlinear ordinary differential equation of fractional order with a new independent variable. The derivative corresponding to time fractional in the reduced equation is usually known as the Erdélyi-Kober fractional derivative.
MSC:
35R11Fractional partial differential equations
35Q53KdV-like (Korteweg-de Vries) equations
35Q35PDEs in connection with fluid mechanics
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