NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY

doi:10.1007/s10473-021-0518-1

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1699-1718.doi: 10.1007/s10473-021-0518-1

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NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY

Ravi AGARWAL^1,2, Ricardo ALMEIDA³, Snezhana HRISTOVA⁴, Donal O'REGAN⁵

1. Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA;
2. Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA;
3. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal;
4. Department of Applied Mathematics and Modeling, University of Plovdiv Paisii Hilendarski, Plovdiv, Bulgaria;
5. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Received:2019-09-18 Revised:2020-08-20 Online:2021-10-25 Published:2021-10-21
Contact: Ravi AGARWAL E-mail:Ravi.Agarwal@tamuk.edu
Supported by:
R. Almeida was supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UIDB/04106/2020, and Fund Scientific Research MU21FMI007, University of Plovdiv "Paisii Hilendarski".

Abstract

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.

Key words: non-instantaneous impulses, Caputo fractional differential equations, practical stability

CLC Number:

34A08

Ravi AGARWAL, Ricardo ALMEIDA, Snezhana HRISTOVA, Donal O'REGAN. NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY[J].Acta mathematica scientia,Series B, 2021, 41(5): 1699-1718.

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References

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NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY

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