STABILITY PROPERTIES IN IMPULSIVE DIFFERENTIAL SYSTEMS OF NON-INTEGER ORDER

Kang, Bowon;Koo, Namjip

• Received : 2018.02.13
• Accepted : 2018.04.09
• Published : 2019.01.01
• 174 4

Abstract

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

Keywords

aimpulsive fractional differential equation;Mittag-Leffler system;impulsive fractional comparison principle;piecewise continuous auxiliary function

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)