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Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators

Author

Listed:
  • Michal Fec̆kan

    (Comenius University
    Slovak Academy of Sciences)

  • JinRong Wang

    (Guizhou University)

  • Yong Zhou

    (Xiangtan University)

Abstract

The paper is concerned with the controllability of fractional functional evolution equations of Sobolev type in Banach spaces. With the help of two new characteristic solution operators and their properties, such as boundedness and compactness, we present the controllability results corresponding to two admissible control sets via the well-known Schauder fixed point theorem. Finally, an example is given to illustrate our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:1:d:10.1007_s10957-012-0174-7
    DOI: 10.1007/s10957-012-0174-7
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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. JinRong Wang & Zhenbin Fan & Yong Zhou, 2012. "Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 292-302, July.
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    Cited by:

    1. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. 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.
    3. Amar Debbouche & Juan J. Nieto & Delfim F. M. Torres, 2017. "Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 7-31, July.
    4. 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.
    5. Yao-Qun Wu & Jia Wei He, 2022. "Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 79-101, October.
    6. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    7. Rafał Kamocki & Marek Majewski, 2017. "On the Existence and Continuous Dependence on Parameter of Solutions to Some Fractional Dirichlet Problem with Application to Lagrange Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 32-46, July.
    8. Revathi, P. & Sakthivel, R. & Ren, Yong, 2016. "Stochastic functional differential equations of Sobolev-type with infinite delay," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 68-77.

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