Homotopy analysis method for Non-Markovian processes in active matter

We solve the Fokker-Planck (FP) equation for active non-Markovian and quasi-Markovian processes using the homotopy analysis method, and provide analytical expressions for classic mean values as a series in time. For non-Markovian processes we show that the solution is equivalent to a Dyson series in the Fokker-Planck operator. As an example, the active particles case with color noise in an arbitrary potential is solved. Our analytical results were compared to Brownian dynamics simulations showing a good agreement.