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Infinite Interval Problems for Fractional Evolution Equations

Author

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  • Yong Zhou

    (Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China)

Abstract

In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer fractional derivative. By using the generalized Ascoli–Arzelà theorem and some new techniques, we prove the existence of mild solutions of Hilfer fractional evolution equations when the semigroup is compact as well as noncompact. In addition, an example is provided to illustrate the results.

Suggested Citation

  • Yong Zhou, 2022. "Infinite Interval Problems for Fractional Evolution Equations," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:900-:d:769060
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Daliang Zhao, 2023. "Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay," Mathematics, MDPI, vol. 11(19), pages 1-19, September.

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