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Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators

Author

Listed:
  • Y. K. Chang

    (Lanzhou Jiaotong University)

  • W. S. Li

    (Lanzhou Jiaotong University)

Abstract

This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed-point theorem for condensing maps combined with theories of analytic resolvent operators, we prove some existence theorems. As an application of these main theorems, some practical consequences are derived.

Suggested Citation

  • Y. K. Chang & W. S. Li, 2010. "Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 445-459, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9612-6
    DOI: 10.1007/s10957-009-9612-6
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    References listed on IDEAS

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    1. Y.-K. Chang & J. J. Nieto & W.-S. Li, 2009. "On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 431-442, March.
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