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Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

Author

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  • Selvaraj Suganya

    (Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore 641 042, Tamil Nadu, India)

  • Mani Mallika Arjunan

    (Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore 641 042, Tamil Nadu, India)

Abstract

In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI) with state-dependent delay (SDD) in Banach spaces. An example is provided to illustrate the obtained abstract results.

Suggested Citation

  • Selvaraj Suganya & Mani Mallika Arjunan, 2017. "Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay," Mathematics, MDPI, vol. 5(1), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:1:p:9-:d:88738
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    References listed on IDEAS

    as
    1. Alka Chadha & Dwijendra N. Pandey, 2014. "Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay," International Journal of Differential Equations, Hindawi, vol. 2014, pages 1-10, May.
    2. Zhi-Wei Lv & Bao-Feng Chen, 2014. "Existence and Uniqueness of Positive Solutions for a Fractional Switched System," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    3. Wang, JinRong & Ibrahim, Ahmed Gamal & Fečkan, Michal, 2015. "Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 103-118.
    4. Jaydev Dabas & Archana Chauhan & Mukesh Kumar, 2011. "Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-20, October.
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