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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

Volume 110 / 2014

Zuomao Yan, Hongwu Zhang Annales Polonici Mathematici 110 (2014), 143-169 MSC: Primary 34A37, 34A60; Secondary 35R12, 26A33. DOI: 10.4064/ap110-2-4

Abstract

We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an $\alpha $-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the $\alpha $-resolvent operator. An example is given to illustrate the theory.

Authors

  • Zuomao YanDepartment of Mathematics
    Hexi University
    Zhangye, Gansu 734000, P.R. China
    e-mail
  • Hongwu ZhangDepartment of Mathematics
    Hexi University
    Zhangye, Gansu 734000, P.R. China

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