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.

A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces

“…Indeed, FDEs have a large flood of applications in different scopes such as chemistry, physics, finance, engineering, and infectious disease. The combination of FDEs and other analytical and numerical methods can be found in many works such as impulsive FDEs [6,7], implicit hybrid FDEs [8][9][10], mathematical modelings with the help of FDEs [11][12][13][14][15], neutral FDEs [16,17], p-Laplacian FDEs [18], variable order time-fractional FDEs [19], random and fuzzy FDEs [20,21], integro-differential inclusions [22,23], and references therein.…”