scholarly journals Existence of Solution of Neutral Fractional Impulsive Differential Equations with Infinite Delay

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
K. Hilal ◽  
Y. Allaoui
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Impulsive Differential Equations ◽  
Existence Of Solution

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

scholarly journals On the Practical Stability of Impulsive Differential Equations with Infinite Delay in Terms of Two Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Wu ◽  
Jing Han ◽  
Xiushan Cai
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Infinite Delay ◽  
Impulsive Differential Equations ◽  
Practical Stability ◽  
Stability Criteria ◽  
Razumikhin Technique ◽  
Two Measures

We consider the practical stability of impulsive differential equations with infinite delay in terms of two measures. New stability criteria are established by employing Lyapunov functions and Razumikhin technique. Moreover, an example is given to illustrate the advantage of the obtained result.

Existence of Solution for Second Order Impulsive Differential Equations with Mixed Boundary Conditions

2013 ◽  
Vol 411-414 ◽  
pp. 1396-1399
Author(s):  
Li Zhao Yan ◽  
Jian Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Variational Methods ◽  
Mixed Boundary ◽  
Impulsive Differential Equations ◽  
Mixed Boundary Conditions ◽  
Existence Of Solution ◽  
Second Order

In this paper, we use variational methods to investigate the solutions of impulsive differential equations with mixed boundary conditions. The conditions for the existence of solution are established. The main results are also demonstrated with examples.

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