Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation

Abstract In this study, solutions to the nonlinear time-dependent fractional reaction–diffusion equation with conformal fractional derivative is considered. In the first part of the manuscript, we reduce the fractional equation to a traditional differential equation using the fractional complex transformation. Two cases where the exact solution exists are then presented. One of these solutions is used to model experimental data showing anomalous diffusion in freestanding graphene. In the second part, we study the travelling solutions and present two cases: Canonical-like transformation method and complete discrimination system for polynomial method.