On the invariant analysis and integrability of the time-fractional potential KdV equation

Abstract

We perform a Lie point symmetry analysis of a time-fractional potential Korteweg–de Vries (FP-KdV) equation with the Riemann–Liouville derivative. By transforming the dependent variable, we map the time-fractional FP-KdV equation to a nonlinear ordinary differential equation (ODE) of fractional order using underlying symmetry generators. We obtain the derivative in the Erdélyi–Kober operator. We then construct the solution of the reduced fractional ODE by applying the power series method. The conservation laws (CLs) for the time-fractional FP-KdV equation are determined via Ibragimov’s non-local conservation method to time-fractional partial differential equations (FPDEs). Solutions for FPDEs via CLs have yet to be explored. Additionally, we present graphical representations of the results obtained using the power series solution method.