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Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)

Author

Listed:
  • Jia Wei He

    (Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

  • Yong Liang

    (Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China)

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Yong Zhou

    (Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α ∈ ( 1 , 2 ) . The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem.

Suggested Citation

  • Jia Wei He & Yong Liang & Bashir Ahmad & Yong Zhou, 2019. "Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:209-:d:208708
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    References listed on IDEAS

    as
    1. Yong Zhou & Jia Wei He & Bashir Ahmad & Ahmed Alsaedi, 2018. "Existence and Attractivity for Fractional Evolution Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, January.
    2. Dimplekumar N. Chalishajar, 2012. "Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 672-684, August.
    3. Fan, Zhenbin, 2014. "Characterization of compactness for resolvents and its applications," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 60-67.
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    Citations

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    Cited by:

    1. Mohan Raja, M. & Vijayakumar, V., 2022. "Existence results for Caputo fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order r ∈ (1,2) with sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. 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.
    4. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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