Fractal-view analysis of local fractional Fokker–Planck equation occurring in modelling of particle’s Brownian motion

In this paper, the solution and behaviour of local fractional Fokker–Planck equation (LFFPE) is investigated in fractal media. For this purpose, the local fractional homotopy perturbation Elzaki transform method (LFHPETM) is proposed and utilized to explore the solution of LFFPE. The proposed scheme is a merger of well known local fractional homotopy perturbation technique and recently introduced local fractional Elzaki transform (LFET). The convergence and uniqueness analyses for LFHPETM solution of the general partial differential equation is also presented along with the computational procedure of this new hybrid combination. Three examples of LFFPE are illustrated to depict the applicability of the employed method with graphical simulations on Cantor set. The copulation of LFET with local fractional homotopy perturbation method (LFHPM) efficiently provides the faster solution for LFFPE in a fractal domain as compared to the LFHPM. Furthermore, the achieved solutions are also in a good match with existing solutions. The 3D behavior of solutions of LFFPEs are presented for fractal order ln 2 / ln 3 . Figures illustrate the 3D surface graphics of solutions with respect to input variables.