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Non-Instantaneous Impulsive Fractional Differential Equations with State Dependent Delay and Practical Stability

Authors
  • Agarwal, Ravi1, 2
  • Almeida, Ricardo3
  • Hristova, Snezhana4
  • O’Regan, Donal5
  • 1 Texas A & M University-Kingsville, Kingsville, TX, 78363, USA , Kingsville (United States)
  • 2 Florida Institute of Technology, Melbourne, FL, 32901, USA , Melbourne (United States)
  • 3 University of Aveiro, Aveiro, Portugal , Aveiro (Portugal)
  • 4 University of Plovdiv Paisii Hilendarski, Plovdiv, Bulgaria , Plovdiv (Bulgaria)
  • 5 National University of Ireland, Galway, Ireland , Galway (Ireland)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 29, 2021
Volume
41
Issue
5
Pages
1699–1718
Identifiers
DOI: 10.1007/s10473-021-0518-1
Source
Springer Nature
Keywords
Disciplines
  • Article
License
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Abstract

Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay, depending on both the time and the state variable. The case when the lower limit of the Caputo fractional derivative is fixed at the initial time, and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied. Practical stability properties, based on the modified Razumikhin method are investigated. Several examples are given in this paper to illustrate the results.

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