Fractional Brownian Motion for a System of Fuzzy Fractional Stochastic Differential Equation

Abstract

We study fractional Brownian motion– (FBM–) driven fuzzy stochastic fractional evolution equations. These equations can be used to model fuzziness, long-range dependence, and unpredictability in hybrid real-world systems. Under various assumptions regarding the coefficients, we investigate the existence-uniqueness of the solution using an approximation method to the fractional stochastic integral. We can solve an equation with linear coefficients, for example, in financial models Application to a model of population dynamics is also illustrated. An example is propounded to show the applicability of our results.