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Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function

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  • Balasubramaniam, P.
  • Tamilalagan, P.

Abstract

In this paper, we formulate a new set of sufficient conditions for the approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay in Hilbert space. Bohnenblust–Karlin’s fixed point theorem, Mainardi’s function, fractional calculus and operator semigroups are used to establish the results under the assumption that the corresponding linear system is approximately controllable. In the end, an example is provided to illustrate the applicability of the obtained theoretical results.

Suggested Citation

  • Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:232-246
    DOI: 10.1016/j.amc.2015.01.035
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Sivajiganesan Sivasankar & Ramalingam Udhayakumar, 2022. "Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(12), pages 1-19, June.
    2. Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    3. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.
    5. Lu, Liang & Liu, Zhenhai & Bin, Maojun, 2016. "Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 201-212.
    6. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Lu, Liang & Liu, Zhenhai, 2015. "Existence and controllability results for stochastic fractional evolution hemivariational inequalities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1164-1176.
    8. Ge, Fu-Dong & Zhou, Hua-Cheng & Kou, Chun-Hai, 2016. "Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 107-120.
    9. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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