Stability analysis of Atangana-Baleanu fractional stochastic differential systems with impulses. (English) Zbl 1518.93146
Summary: This paper is devoted to exploring a new class of Atangana-Baleanu fractional stochastic differential systems driven by fractional Brownian motion with non-instantaneous impulsive effects. Using resolvent family, fixed point technique, and fractional calculus, we analysed the existence and uniqueness of the mild solution. Moreover, we discussed the stability criteria for the proposed problem. A numerical example is given to illustrate the theoretical results.
MSC:
| 93E15 | Stochastic stability in control theory |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34A08 | Fractional ordinary differential equations |
| 93C27 | Impulsive control/observation systems |
| 34A37 | Ordinary differential equations with impulses |
| 60G22 | Fractional processes, including fractional Brownian motion |
Keywords:
stochastic system; Atangana-Baleanu fractional derivative; fractional Brownian motion; non-instantaneous impulses; stabilityReferences:
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