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Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

Author

Listed:
  • Abdelhamid Bensalem

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
    These authors contributed equally to this work.)

  • Abdelkrim Salim

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
    Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
    These authors contributed equally to this work.)

  • Mouffak Benchohra

    (Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
    These authors contributed equally to this work.)

  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
    These authors contributed equally to this work.)

Abstract

In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo’s fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration.

Suggested Citation

  • Abdelhamid Bensalem & Abdelkrim Salim & Mouffak Benchohra & Michal Fečkan, 2023. "Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1667-:d:1112206
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    References listed on IDEAS

    as
    1. Sumit Arora & Manil T. Mohan & Jaydev Dabas, 2023. "Finite-Approximate Controllability of Impulsive Fractional Functional Evolution Equations of Order $$1," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 855-890, June.
    2. Mouffak Benchohra & Fatima Bouazzaoui & Erdal Karapinar & Abdelkrim Salim, 2022. "Controllability of Second Order Functional Random Differential Equations with Delay," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
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