Group formalism of Lie transformations to time-fractional partial differential equations

A systematic method is given to derive Lie point symmetries of time-fractional partial differential equation with Riemann-Liouville fractional derivative and its applicability illustrated through (i) time-fractional diffusive equation and (ii) time-fractional cylindrical Korteweg-de Vries equation. Using the Lie point symmetries obtained, we show that each of them has been transformed into ordinary differential equation of fractional order with a new independent variable. We also explain how exact or invariant solutions can be derived from the obtained point symmetries.