• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.243-253
• /
• 2003

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• 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.

• Explosives and Blasting
• /
• v.15 no.4
• /
• pp.11-17
• /
• 1997

Impulsive vibration velocity is monitored at the surface and the boundary surface of rocks as various impulsive forces of horizontal and vertical directions were given to rocks which had difference in uniaxial compressive strength for investigate to the vibration velocity of rocks according to the impulsive direction and the monitoring site. The vibration velocity of the boundary surface of rocks was about 2.9 times or much larger than that of the surface at the same scaled distance in the case of horizontal impulsive forces, and was above 4.2 times in the case of vertical impulsive forces. The attenuation exponents of the vibration velocity equations in the surface and the boundary surface of rocks make a vast difference with the impulsive directions, but is makes little difference in the case of the same impulsive direction. The ratio of vibration constants of the surface to the boundary surface of rocks is that square and cube root scaled equation is a range of 2.7∼3.0 and 4.9∼5.0 respectively in the case of horizontal impulsive forces, and is a range of 4.2∼5.7 and 7.7∼11.5 respectively in the case of vertical impulsive forces.

• Kyungpook Mathematical Journal
• /
• v.48 no.4
• /
• pp.593-611
• /
• 2008

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.3_4
• /
• pp.151-184
• /
• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.111-123
• /
• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.515-521
• /
• 2016

This paper deals with linear impulsive differential equations with non-integer orders. We provide the explicit representation of solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.225-247
• /
• 2010

In this paper, we establish a two-competitive-prey and one-predator Holling type II system by introducing a proportional periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for the predator at different fixed time. We show the boundedness of the system and find conditions for the local and global stabilities of two-prey-free periodic solutions by using Floquet theory for the impulsive differential equation, small amplitude perturbation skills and comparison techniques. Also, we prove that the system is permanent under some conditions and give sufficient conditions under which one of the two preys is extinct and the remaining two species are permanent. In addition, we take account of the system with seasonality as a periodic forcing term in the intrinsic growth rate of prey population and then find conditions for the stability of the two-prey-free periodic solutions and for the permanence of this system. We discuss the complex dynamical aspects of these systems via bifurcation diagrams.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.11 no.9
• /
• pp.406-413
• /
• 2001

The current study depicts and experimental work of the impulsive wave discharged from the exit of several kinds of right-angle bend pipes, which are attached to the open end of a simple shock tube. The weak normal shock wave with Mach number from 1.02 to 1.20 is employed to obtain the impulsive wave propagating outside the exit of the pipe bends. The experimental data of the magnitude of the impulsive wave and its propagation directivity are analyzed to characterize the impulsive waves discharged from the right-angle bend pipes and compared with those from a straight pipe. The impulsive waves are visualized by a Schlieren optical system. A computation work using the two-dimensional, unsteady, compressible Euler equation is also carried out to represent the experimented impulsive waves. The results obtained show that a right-angle miter bend considerably reduces the magnitude of the impulsive wave and its directivity toward to the pipe axis, compared with the straight pipe. It is believed that the right angle miter bend pipe can play a role of passive control agianst the impulsive wave.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.405-417
• /
• 2005

In this paper, the oscillation and asymptotic stability behavior of a third order linear impulsive equation are investigated. A lemma is presented to deal with the sign relation of the nonoscillatory solutions and their derived functions. By the lemma explicit sufficient conditions are obtained for all solutions either oscillating or asymptotically tending to zero. Two illustrative examples are proposed to demonstrate the effectiveness of the conditions.