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Characterization of compactness for resolvents and its applications

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  • Fan, Zhenbin

Abstract

In this paper, we derive some characterizations of compactness for resolvents as well as the subordination principle associated with the compactness. As applications, we obtain the existence of fractional evolution equations by using Schauder’s fixed point theorem. A simple example about fractional heat equation is also given to illustrate our theory.

Suggested Citation

  • Fan, Zhenbin, 2014. "Characterization of compactness for resolvents and its applications," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 60-67.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:60-67
    DOI: 10.1016/j.amc.2014.01.051
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    Cited by:

    1. Shouguo Zhu & Zhenbin Fan & Gang Li, 2017. "Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 47-64, July.
    2. 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.
    3. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    4. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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