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Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators

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  • 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)

Abstract

In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2074-:d:839565
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    References listed on IDEAS

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    1. R. Ganesh & R. Sakthivel & N. I. Mahmudov & S. M. Anthoni, 2013. "Approximate Controllability of Fractional Integrodifferential Evolution Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    2. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    3. 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.
    4. Fang Li & Ti-Jun Xiao & Hong-Kun Xu, 2012. "On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, May.
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    Cited by:

    1. 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.
    2. 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.

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