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Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions

Author

Listed:
  • Nawapol Phuangthong

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while Martelli’s fixed point theorem, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results.

Suggested Citation

  • Nawapol Phuangthong & Sotiris K. Ntouyas & Jessada Tariboon & Kamsing Nonlaopon, 2021. "Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:615-:d:516996
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    References listed on IDEAS

    as
    1. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    2. 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.
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