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The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators

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  • P. Balasubramaniam

    (Gandhigram Rural Institute - Deemed University)

  • P. Tamilalagan

    (Gandhigram Rural Institute - Deemed University)

Abstract

In this manuscript, we investigate the solvability and optimal controls for impulsive fractional stochastic integro-differential equations in Hilbert space. Sufficient conditions are obtained for the existence of mild solution of the considered system by using analytic resolvent operators, the uniform continuity of the resolvent, and Leray–Schauder fixed point theorem. Then, the existence of optimal controls is discussed for the considered system. Finally, the obtained theoretical result is validated through an example.

Suggested Citation

  • P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0865-6
    DOI: 10.1007/s10957-016-0865-6
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    References listed on IDEAS

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    1. JinRong Wang & Yong Zhou & Milan Medveď, 2012. "On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 31-50, January.
    2. Fan, Zhenbin, 2014. "Characterization of compactness for resolvents and its applications," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 60-67.
    3. N. Sukavanam & Surendra Kumar, 2011. "Approximate Controllability of Fractional Order Semilinear Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 373-384, November.
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    Cited by:

    1. A. M. A. El-Sayed & Hoda A. Fouad, 2021. "On a Coupled System of Stochastic It o ^ -Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions," Mathematics, MDPI, vol. 9(20), pages 1-14, October.
    2. Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Zuomao Yan & Li Han, 2019. "Optimal Mild Solutions for a Class of Nonlocal Multi-Valued Stochastic Delay Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1053-1075, June.
    4. Surendra Kumar & Shobha Yadav, 2021. "Infinite-delayed stochastic impulsive differential systems with Poisson jumps," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 344-362, June.
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    6. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.

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