Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (1): 105-113.

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Existence and Uniqueness of the Mild Solutions for a Class of Fractional Non-Autonomous Evolution Equations with Impulses

Bo Zhu1,*(),Lishan Liu2   

  1. 1 School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014
    2 School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2017-09-14 Online:2019-02-26 Published:2019-03-12
  • Contact: Bo Zhu E-mail:zhubo207@163.com
  • Supported by:
    the PSDPHESTP(J16LI14);the NSFC(11871302)

Abstract:

In this paper, we consider a class of fractional non-autonomous evolution equations with impulses and delay. By the generalized Banach fixed point theorem, we obtain some new results on the existence and uniqueness of the mild solution. An explicit iterative scheme for the mild solution and an error estimate of the approximation sequence for the initial value problem are also derived. Moreover, the unique mild solution of the problem is continuously dependent on the initial value.

Key words: Fractional non-autonomous evolution equations, Non-instantaneous impulse, Resolvent operator, Generalized Banach fixed point theorem

CLC Number: 

  • O175
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