Lie symmetry analysis, conservation laws and analytical solutions of a time-fractional generalized KdV-type equation

Abstract

Under investigation in this work is the time-fractional generalized KdV-type equation, which occurs in different contexts in mathematical physics. Lie group analysis method is presented to explicitly study its vector fields and symmetry reductions. Furthermore, two straightforward methods are employed to consider its travelling wave solutions and power series solutions, respectively. Finally, based on the new conservation theorem, conservation laws of the equation are well constructed with a detailed derivation.