p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses

Ravi Agarwal; Snezhana Hristova; Donal O’Regan

doi:10.1007/s12190-016-1030-y

p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses

Ravi Agarwal
, Snezhana Hristova
, Donal O’Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

10 Citations (Scopus)

Abstract

Stability of Caputo fractional differential equations with impulses occurring at random moments and with non-instantaneous time of their action is studied. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of the zero solution is defined and studied when the waiting time between two consecutive impulses is exponentially distributed and the length of the action of any impulse is initially given. The argument is based on Lyapunov functions. Some examples are given to illustrate our results.

Original language	English
Pages (from-to)	149-174
Number of pages	26
Journal	Journal of Applied Mathematics and Computing
Volume	55
Issue number	1-2
DOIs	https://doi.org/10.1007/s12190-016-1030-y
Publication status	Published - 1 Oct 2017

Keywords

Impulsive fractional differential equations
Non-instantaneous impulses
Random moments of impulses
p-Moment exponential stability

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10.1007/s12190-016-1030-y

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title = "p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses",

abstract = "Stability of Caputo fractional differential equations with impulses occurring at random moments and with non-instantaneous time of their action is studied. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of the zero solution is defined and studied when the waiting time between two consecutive impulses is exponentially distributed and the length of the action of any impulse is initially given. The argument is based on Lyapunov functions. Some examples are given to illustrate our results.",

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author = "Ravi Agarwal and Snezhana Hristova and Donal O{\textquoteright}Regan",

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AU - Agarwal, Ravi

AU - Hristova, Snezhana

AU - O’Regan, Donal

PY - 2017/10/1

Y1 - 2017/10/1

N2 - Stability of Caputo fractional differential equations with impulses occurring at random moments and with non-instantaneous time of their action is studied. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of the zero solution is defined and studied when the waiting time between two consecutive impulses is exponentially distributed and the length of the action of any impulse is initially given. The argument is based on Lyapunov functions. Some examples are given to illustrate our results.

AB - Stability of Caputo fractional differential equations with impulses occurring at random moments and with non-instantaneous time of their action is studied. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of the zero solution is defined and studied when the waiting time between two consecutive impulses is exponentially distributed and the length of the action of any impulse is initially given. The argument is based on Lyapunov functions. Some examples are given to illustrate our results.

KW - Impulsive fractional differential equations

KW - Non-instantaneous impulses

KW - Random moments of impulses

KW - p-Moment exponential stability

UR - https://www.scopus.com/pages/publications/84977086487

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DO - 10.1007/s12190-016-1030-y

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SP - 149

EP - 174

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 1-2

ER -

p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses

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Keywords

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