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A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators

Author

Listed:
  • Sivajiganesan Sivasankar

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India)

  • Ramalingam Udhayakumar

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India)

  • Muchenedi Hari Kishor

    (Department of Analytics, School of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India)

  • Sharifah E. Alhazmi

    (Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia)

  • Shrideh Al-Omari

    (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Amman 11134, Jordan)

Abstract

This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas of the study are illustrated by using ideas from fractional calculus, the fixed point technique, and measures of noncompactness. Then, the authors establish new criteria for the mild existence of solutions and derive fundamental characteristics of the nonlocal controllability of a system. In addition, researchers offer theoretical and real-world examples to demonstrate the effectiveness and suitability of our suggested solutions.

Suggested Citation

  • Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Muchenedi Hari Kishor & Sharifah E. Alhazmi & Shrideh Al-Omari, 2022. "A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:159-:d:1018107
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    References listed on IDEAS

    as
    1. 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).
    2. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. 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.
    4. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Velmurugan Subramanian & Ghada AlNemer & Ahmed M. Elshenhab, 2022. "Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    5. Mohamed Bouaouid & Mohamed Hannabou & Khalid Hilal & Nasser Saad, 2020. "Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces," Journal of Mathematics, Hindawi, vol. 2020, pages 1-6, February.
    6. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
    7. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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