Approximate controllability of Atangana-Baleanu fractional stochastic differential systems with non-Gaussian process and impulses. (English) Zbl 07920717
Summary: This paper aims to investigate a new class of Atangana-Baleanu fractional stochastic differential systems under the influence of the Rosenblatt process and non-instantaneous impulses. We analyze the existence and uniqueness of piecewise continuous mild solutions by using the fixed point method, fractional calculus, and resolvent family. Further, we define a new piecewise control function and investigate the approximate controllability results for the proposed problem. Finally, the main results are validated with the aid of an example.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 26A33 | Fractional derivatives and integrals |
| 93B05 | Controllability |
| 60G12 | General second-order stochastic processes |
Keywords:
stochastic systems; Atangana-Baleanu fractional derivatives; impulses; approximate controllability; Rosenblatt processReferences:
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