A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator

This endeavour provides a new instance of understanding the velocity of a particle in Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new mathematical tool invoked by Yang-Abdel-Aty-Cattani (YAC) to solve the fractional derivative on Fokker-Plank equation. The HPTM and RPSMs, are used to obtain the solution in terms of Prabhakar function. Numerical examples to extend these ideas and to establish the capability and truthfulness of the proposed method, which makes use of YAC-fractional derivative, is also briefly sketched. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.