Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H^∈(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we discuss the existence of a piecewise co...

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Bibliographic Details
Published in:Fractal and fractional 2023-01, Vol.7 (2), p.104
Main Authors: Hakkar, Naima, Dhayal, Rajesh, Debbouche, Amar, Torres, Delfim F. M.
Format: Article
Language:English
Subjects:
approximate controllability
Control theory
Controllability
Fractional calculus
fractional stochastic delay system
Hilbert space
Hypotheses
impulsive effects
mixed noise
Random variables
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Summary:We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H^∈(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we discuss the existence of a piecewise continuous mild solution for the proposed system. Moreover, under appropriate conditions, we investigate the approximate controllability of the considered system. Finally, the main results are demonstrated with an illustrative example.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7020104