SOLUTION TO THE FOKKER-PLANCK EQUATION USING HOMOTOPIC TECHNIQUE

We find the general solution to the Fokker-Planck equation using homotopic methods. This result is represented as a series solution in time. The series coefficients are determined as phase-space derivate operators. In addition, the general formalism is used to find mean values (variance and mean-square displacements) for the case of active Brownian particles on Euclidian and non-Euclidian spaces and under external fields. The theoretical results are validated using Brownian Dynamics simulations.