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Approximate Controllability of Semilinear Fractional Stochastic Dynamic Systems with Nonlocal Conditions in Hilbert Spaces

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Abstract

A class of dynamic control systems described by semilinear fractional stochastic differential equations of order 1 < q < 2 with nonlocal conditions in Hilbert spaces is considered. Using solution operator theory, fractional calculations, fixed-point technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for nonlocal approximate controllability of semilinear fractional stochastic dynamic systems is formulated and proved by assuming the associated linear system is approximately controllable. As a remark, the conditions for the exact controllability results are obtained. Finally, an example is provided to illustrate the obtained theory.

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Authors and Affiliations

  1. Laboratory of Stochastic Models, Statistic and Applications, Tahar Moulay University, PO.Box 138, En-Nasr, 20000, Saida, Algeria

    Toufik Guendouzi & Souad Farahi

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  1. Toufik Guendouzi
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  2. Souad Farahi
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Correspondence to Toufik Guendouzi.

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Guendouzi, T., Farahi, S. Approximate Controllability of Semilinear Fractional Stochastic Dynamic Systems with Nonlocal Conditions in Hilbert Spaces. Mediterr. J. Math. 13, 637–656 (2016). https://doi.org/10.1007/s00009-014-0503-1

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  • DOI: https://doi.org/10.1007/s00009-014-0503-1

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