68 research outputs found

    Controllability Problem of Fractional Neutral Systems: A Survey

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    The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems

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

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    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)\hat{\cal H} \in ( 1/2, 1). Using fixed point techniques, a qq-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.Comment: Please cite this paper as follows: Hakkar, N.; Dhayal, R.; Debbouche, A.; Torres, D.F.M. Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects. Fractal Fract. 2023, 7, 104. https://doi.org/10.3390/fractalfract702010

    On Approximately Controlled Systems

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    Controllability of impulsive neutral stochastic integro-differential systems driven by FBM with unbounded delay

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    In this paper we study the controllability results of impulsive neutral stochastic functional integrodifferential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are obtained by using stochastic analysis and a fixed-point strategy. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained
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