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

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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.

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Authors and Affiliations

  1. School of Mathematics, Physics & Software Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Y. K. Chang & W. S. Li

Authors
  1. Y. K. Chang
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  2. W. S. Li
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Correspondence to Y. K. Chang.

Additional information

Communicated by F. Zirilli.

Y.K. Chang is supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10901075), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) by Lanzhou Jiaotong University.

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Chang, Y.K., Li, W.S. Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators. J Optim Theory Appl 144, 445–459 (2010). https://doi.org/10.1007/s10957-009-9612-6

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