Existence and computational results to Volterra–Fredholm integro-differential equations involving delay term

2021 ◽  
Vol 40 (8) ◽  
Author(s):  
Rohul Amin ◽  
Ali Ahmadian ◽  
Nasser Aedh Alreshidi ◽  
Liping Gao ◽  
Mehdi Salimi
Keyword(s):  
Differential Equations ◽  
Computational Results ◽  
Delay Term

scholarly journals Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Higher Order ◽  
Middle Term ◽  
Delay Term ◽  
Integral Averaging Technique ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Comparison Technique ◽  
Higher Order Differential Equations

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.

scholarly journals Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Peiguang Wang ◽  
Yan Xu
Keyword(s):  
Differential Equations ◽  
Operator Theory ◽  
Delay Differential Equations ◽  
Averaging Principle ◽  
Neutral System ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Delay Term ◽  
Delay Differential

In this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition. By using the linear operator theory, we deal with the difficulty brought by delay term of the neutral system and obtain the conclusion that the solutions of neutral stochastic delay differential equations with impulses converge to the solutions of the corresponding averaged stochastic delay differential equations without impulses in the sense of mean square and in probability. At last, an example is presented to show the validity of the proposed theories.

scholarly journals Maximal monotone model with delay term of convolution

2005 ◽  
Vol 2005 (4) ◽  
pp. 437-453 ◽  
Author(s):  
Claude-Henri Lamarque ◽  
Jérôme Bastien ◽  
Matthieu Holland
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Maximal Monotone ◽  
Model Description ◽  
Delay Term ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mechanical Models

Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics) or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description) with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction), we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given.

scholarly journals A Note on Homogenization of Ordinary Differential Equations with Delay Term

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 889-890 ◽  
Author(s):  
Marcus Waurick ◽  
Michael Kaliske
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Delay Term ◽  
Equations With Delay

scholarly journals Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 782
Author(s):  
Hernán Darío Toro-Zapata ◽  
Carlos Andrés Trujillo-Salazar ◽  
Edwin Mauricio Carranza-Mayorga
Keyword(s):  
Mathematical Model ◽  
T Cell ◽  
Differential Equations ◽  
T Cell Activation ◽  
Cell Activation ◽  
Cd4 T Cell ◽  
Human Immune System ◽  
Hiv Viral Load ◽  
Delay Term ◽  
Linear Differential

A mathematical model composed of two non-linear differential equations that describe the population dynamics of CD4 T-cells in the human immune system, as well as viral HIV viral load, is proposed. The invariance region is determined, classical equilibrium stability analysis is performed by using the basic reproduction number, and numerical simulations are carried out to illustrate stability results. Thereafter, the model is modified with a delay term, describing the time required for CD4 T-cell immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations. For the new model, equilibriums are determined, their local stability is examined, and results are studied by way of numerical simulation.

scholarly journals Stability conditions for scalar delay differential equations with a non-delay term

2015 ◽  
Vol 250 ◽  
pp. 157-164 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Stability Conditions ◽  
Delay Term ◽  
Delay Differential

Computational Treatment of First Order Delay Differential Equations Using Hybrid Extended Second Derivative Block Backward Differentiation Formulae

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
C. Chibuisi ◽  
Bright Okore Osu ◽  
C. Olunkwa ◽  
S. A. Ihedioha ◽  
S. Amaraihu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Derivative ◽  
Delay Term ◽  
First Order ◽  
Block Form ◽  
Collocation Approach ◽  
Backward Differentiation Formulae ◽  
Delay Differential ◽  
Step Number

This paper considers the computational solution of first order delay differential equations (DDEs) using hybrid extended second derivative backward differentiation formulae method in block form without the implementation of interpolation techniques in estimating the delay term. By matrix inversion approach, the discrete schemes were obtained through the linear multistep collocation approach from the continuous form of each step number which after implementation strongly revealed the convergence and region of absolute stability of the proposed method. Computational results are presented and compared to the exact solutions and other existing method to demonstrate its efficiency and accuracy.

DECAY AND GROWTH RATES OF SOLUTIONS OF SCALAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY AND STATE DEPENDENT NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. 133-147 ◽  
Author(s):  
JOHN A. D. APPLEBY
Keyword(s):  
Differential Equations ◽  
Growth Rates ◽  
Delay Differential Equations ◽  
Decay Rates ◽  
Stochastic Delay Differential Equations ◽  
Diffusion Term ◽  
Stochastic Delay ◽  
Delay Term ◽  
Unbounded Delay ◽  
Delay Differential

This paper studies the growth and decay rates of solutions of scalar stochastic delay differential equations of Itô type. The equations studied have a linear drift which contains an unbounded delay term, and a nonlinear diffusion term, which depends on the current state only. We show that when the nonlinearity at zero or infinity is sufficiently weak, the same non-exponential decay and growth rates found in the corresponding underlying linear deterministic equation are recovered, in an almost sure sense.

scholarly journals Computation of First order Delay Differential Equations via Simpson Block Method

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Ridwanulahi I Abdulganiy ◽  
Olusheye A Akinfenwa ◽  
Osaretin E Enobabor ◽  
Blessing I Orji ◽  
Solomon A Okunuga
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Step Width ◽  
Block Method ◽  
Delay Term ◽  
First Order ◽  
Collocation Technique ◽  
Delay Differential

A family of Simpson Block Method (SBM) is proposed for the numerical integration of Delay Differential Equations (DDEs). The methods are developed through multistep collocation technique using constant step width. The convergence and accuracy of the methods are established through some standard DDEs in the reviewed literature. Keywords— Block Method, Collocation Technique, Delay Term, Delay Differential Equation, Self Starting.   

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