• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.181-199
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• 2016

In this paper we obtain some retarded integral inequalities involving Stieltjes derivatives and we use our results in the study of various qualitative properties of a certain retarded impulsive differential equation.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.651-659
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• 2014

In this paper we present some Gronwall-tpye inequalities with a non-separable kernel and obtain the explicit estimate for solutions of impulsive differential equations. Furthermore, we give an example to illustrate our results.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.393-400
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• 2011

In this paper we study h-stability for the linear impulsive equations using the notion of kinematical similarity and impulsive integral inequality.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.61-75
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• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.811-819
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• 2013

In this paper we investigate h-stability for linear impulsive equations using the notion of $t_{\infty}$-similarity and an impulsive integral inequality.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.583-590
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• 2015

This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.935-943
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• 2011

We study the h-stability for linear impulsive differential equations and their perturbations by using the impulsive integral inequalities.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.127-147
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• 2019

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.