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Finite-approximate controllability of semilinear fractional stochastic integro-differential equations

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  • Mahmudov, N.I.

Abstract

We introduce the concepts of simultaneous finite dimensional exact and mean square approximate controllability (finite-approximate controllability) in the framework of semilinear fractional stochastic integro-differential evolution Ito equations. Under the approximate controllability of the corresponding linear part we obtain sufficient conditions for the finite-approximate controllability of the semilinear fractional stochastic integro-differential evolution equation. At the end, an example of stochastic heat equation is given to show applicability of our result.

Suggested Citation

  • Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306731
    DOI: 10.1016/j.chaos.2020.110277
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Nazim I. Mahmudov, 2020. "Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 671-686, February.
    4. Liang, Jin & Yang, He, 2015. "Controllability of fractional integro-differential evolution equations with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 20-29.
    5. 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. Dhayal, Rajesh & Malik, Muslim, 2021. "Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. ZOUARI, Farouk & IBEAS, Asier & BOULKROUNE, Abdesselem & CAO, Jinde & AREFI, Mohammad Mehdi, 2021. "Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Nazim I. Mahmudov, 2023. "Mean Square Finite-Approximate Controllability of Semilinear Stochastic Differential Equations with Non-Lipschitz Coefficients," Mathematics, MDPI, vol. 11(3), pages 1-20, January.
    4. Daliang Zhao, 2023. "Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
    5. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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