Ding, Xiao-LiNieto Roig, Juan José2019-10-262019-10-262018-01-16Ding, X.-L.; Nieto, J.J. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications. Entropy 2018, 20, 63http://hdl.handle.net/10347/19948In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained resultsengc 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)http://creativecommons.org/licenses/by/4.0/Multi-time scale fractional stochastic differential equationsFractional Brownian motionFractional stochastic partial differential equationAnalytical solutionjournal article10.3390/e200100631099-4300open access