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Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions

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  • Alka Chadha

    (Indian Institute of Technology Roorkee)

  • Dwijendra N. Pandey

    (Indian Institute of Technology Roorkee)

Abstract

This paper discusses the approximate controllability of a neutral functional integro-differential inclusion involving Caputo fractional derivative in a Hilbert space under the assumptions that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of neutral fractional stochastic functional integro-differential inclusions are formulated and established by utilizing stochastic analysis theory, fractional calculus and the technique of fixed point theorem with analytic compact resolvent operator. An example is also considered for illustrating the discussed theory.

Suggested Citation

  • Alka Chadha & Dwijendra N. Pandey, 2018. "Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions," Journal of Theoretical Probability, Springer, vol. 31(2), pages 705-740, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0732-2
    DOI: 10.1007/s10959-016-0732-2
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    References listed on IDEAS

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    1. Mourad Kerboua & Amar Debbouche & Dumitru Baleanu, 2013. "Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    2. Fang Li & Gaston M. N'Guérékata, 2011. "An Existence Result for Neutral Delay Integrodifferential Equations with Fractional Order and Nonlocal Conditions," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-20, November.
    3. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    4. Zhenhai Liu & Xiuwen Li, 2013. "On the Controllability of Impulsive Fractional Evolution Inclusions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 167-182, January.
    5. Y.-K. Chang & J. J. Nieto & W.-S. Li, 2009. "On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 431-442, March.
    6. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
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