• 충청수학회지
• /
• 제31권1호
• /
• pp.161-166
• /
• 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.

• 대한수학회논문집
• /
• 제35권3호
• /
• pp.879-890
• /
• 2020

In this paper we study the stability properties of solutions of nonlinear impulsive integro-differential systems by using an integral inequality under the stability of the corresponding variational impulsive integro-differential systems. Also, we give examples to illustrate our results.

• 충청수학회지
• /
• 제27권4호
• /
• pp.651-659
• /
• 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.

• 충청수학회지
• /
• 제24권2호
• /
• pp.393-400
• /
• 2011

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

• 충청수학회지
• /
• 제26권4호
• /
• pp.811-819
• /
• 2013

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

• 충청수학회지
• /
• 제28권4호
• /
• pp.583-590
• /
• 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.

• 충청수학회지
• /
• 제24권4호
• /
• pp.935-943
• /
• 2011

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

• Journal of Applied and Pure Mathematics
• /
• 제4권1_2호
• /
• pp.9-26
• /
• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.