scholarly journals On the Oscillation of Conformable Impulsive Vector Partial Differential Equations

2020 ◽  
Vol 76 (1) ◽  
pp. 95-114
Author(s):  
George E. Chatzarakis ◽  
Kandhasamy Logaarasi ◽  
Thangaraj Raja ◽  
Vadivel Sadhasivam
Keyword(s):  
Differential Equations ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Inner Product ◽  
One Dimensional ◽  
Inequality Technique ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Impulsive Differential Inequality

AbstractIn this paper, we study the oscillations of a class of conformable impulsive vector partial functional differential equations. For this class, our approach is to reduce the multi-dimensional oscillation problems to that of one dimensional impulsive delay differential inequalities by applying inner product reducing dimension method and an impulsive differential inequality technique. We provide an example to illustrate the effectiveness of our main results.

scholarly journals Boundary value problem for the second order impulsive delay differential equations

2015 ◽  
Vol 14 (1) ◽  
pp. 27-35
Author(s):  
Lidia Skóra
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Second Order ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

Abstract We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.

scholarly journals A New Comparison Principle for Impulsive Functional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Gang Li ◽  
Weizhong Ling ◽  
Changming Ding
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Systems ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

We establish a new comparison principle for impulsive differential systems with time delay. Then, using this comparison principle, we obtain some sufficient conditions for several stabilities of impulsive delay differential equations. Finally, we present an example to show the effectiveness of our results.

scholarly journals Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pei Cheng ◽  
Fengqi Yao ◽  
Mingang Hua
Keyword(s):  
Comparison Principle ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Delayed Impulses ◽  
Stochastic Functional ◽  
Delay Differential Inequality

The problem of stability for nonlinear impulsive stochastic functional differential equations with delayed impulses is addressed in this paper. Based on the comparison principle and an impulsive delay differential inequality, some exponential stability and asymptotical stability criteria are derived, which show that the system will be stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous stochastic flows. The obtained results complement ones from some recent works. Two examples are discussed to illustrate the effectiveness and advantages of our results.

scholarly journals Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Shiguo Peng ◽  
Liping Yang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Global Exponential Stability ◽  
Functional Differential Equations ◽  
Razumikhin Technique ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

This paper develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mustafa Bahşi ◽  
Mehmet Çevik
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Taylor Series Expansion ◽  
Perturbation Parameter ◽  
Iteration Algorithm ◽  
Proportional Delay ◽  
Pantograph Equation ◽  
Functional Differential ◽  
Delay Differential

The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases.

Asymptotic stability criteria for delay-differential equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 31-44
Author(s):  
L.C. Becker ◽  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
State Variables ◽  
Stability Criteria ◽  
Bounded State ◽  
Functional Differential ◽  
Delay Differential ◽  
Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

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