A fractional model to describe the Brownian motion of particles and its analytical solution

In this article, we apply a relatively modified analytic iterative method for solving a time-fractional Fokker-Planck equation subject to given constraints. The utilized method is a numerical technique based on the generalization of residual error function and then applying the generalized Taylor series formula. This method can be used as an alternative to obtain analytic solutions of different types of fractional partial differential equations such as Fokker-Planck equation applied in mathematics, physics, and engineering. The solutions of our equation are calculated in the form of a rapidly convergent series with easily computable components. The validity, potentiality, and practical usefulness of the proposed method have been demonstrated by applying it to several numerical examples. The results reveal that the proposed methodology is very useful and simple in determination of solution of the Fokker-Planck equation of fractional order.