Lie symmetry analysis of system of nonlinear fractional partial differential equations with Caputo fractional derivative

Abstract

We derive the general prolongation formula for system of fractional partial differential equations (FPDEs) with Caputo derivative involving m dependent variables and n independent variables. A systematic computational method to derive Lie point symmetries of nonlinear FPDEs with Caputo derivative is given, and we illustrate its applicability through system of time fractional diffusion equations and space fractional diffusion equation in Caputo sense. We observe that the set of Lie point symmetries for a given fractional differential equation in Caputo sense is same as the corresponding fractional differential equation in Riemann–Liouville sense. Also we construct their exact solutions in terms of Mittag–Leffler function by using the obtained Lie point symmetries.