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Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

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  • Rodrigo Ponce

Abstract

We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases and

Suggested Citation

  • Rodrigo Ponce, 2016. "Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-15, September.
    • Handle: RePEc:hin:jnlaaa:4567092
    DOI: 10.1155/2016/4567092
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    Cited by:

    1. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Zhiyuan Yuan & Luyao Wang & Wenchang He & Ning Cai & Jia Mu, 2024. "Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    3. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.

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