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Brownian Motion on Cantor Sets

  • Ali Khalili Golmankhaneh , Saleh Ashrafi , Dumitru Baleanu and Arran Fernandez ORCID logo EMAIL logo
Published/Copyright: January 11, 2020

Abstract

In this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

MSC 2010: 28A80; 60G22

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Received: 2018-12-25
Accepted: 2019-06-25
Published Online: 2020-01-11
Published in Print: 2020-05-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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