Search

The first order non-linear neutral differential equations with several non-monotonic delays and several variable coefficients with forcing terms were discussed, also the oscillation behavior of all solutions was investigated where some conditions that guarantee the oscillation for each solution were obtained, illustrative examples related to the obtained results were given. [ABSTRACT FROM AUTHOR]

In this paper we have taken different types of system of fractional delay differential equations with coefficient matrices considering constant as well as variable entries and discussed their oscillatory and non oscillatory behaviour. By giving suitable examples, theoretical results have been justified. [ABSTRACT FROM AUTHOR]

It this paper we study a system of nonlinear delay impulsive fractional differential equations with Riemann-Liouville fractional derivatives taken from both, the unknown function at the present time and the unknown function at the variable time delay. We consider the case when the lower limit of the fractional derivative is changed at each impulsive time point. In the case studied the solution has a singularity at the initial time and any impulsive time point of the impulses. This leads to an appropriate definition of both the initial condition and the impulsive conditions. It is obtained the integral presentation of the solutions on a finite interval. Also, it is definite a special type finite time Lipschitz stability and some sufficient conditions are obtained. [ABSTRACT FROM AUTHOR]

In this note, we present some criteria for the oscillation of second-order neutral delay differential equations. Precisely, we state a result related to the oscillation of unbounded solutions of the equation under consideration and a result related to the oscillation and the convergence for every solution of the same equation. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for existence and uniqueness (EU) of solution for ABC-fractional order neutral differential equations with impulses in Banach space. The results are obtained by using fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper, we want to study the different kinds of solutions of second order nonlinear non-homogeneous neutral delay dynamic equation, classifying these solutions into four classes and obtained conditions for the existence/non-existence of solutions in these classes. Further we have mentioned examples to an important results. [ABSTRACT FROM AUTHOR]

In this study, a matrix method which depends on Laguerre polynomials and with collocation points is developed for solving the approximate solutions of systems of high-order delay differential equations involving variable coefficients and variable delays. These kinds of systems characterized by the present functional delays and which explain many different phenomena and particularly, arise in studies based on biology, physics, chemistry, electrodynmics, and economy and in industrial applications. The proposed method reduces the solution of the mentioned delay system subject to the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Moreover, the approximate solution is obtained in terms of Laguerre polynomials. Besides, some examples along with different error techniques are performed for the illustration of the method’s applicability; the obtained findings are scrutinized and interpreted. [ABSTRACT FROM AUTHOR]

There are almost no results in mathematical literature on the exponential stability of third-order neutral delay differential equations. One of the main purposes of the paper is to fill this gap. We propose an approach to the study of stability for third-order delay differential equations based on AzbelevW-transform. On the basis of these results, new possibilities of stabilization by delay feedback input control are proposed. [ABSTRACT FROM AUTHOR]

An attempt to construct fast Runge–Kutta methods for delay differential equations with distributed delays is made. As a starting point functional continuous methods for general retarded functional differential equations are considered. New explicit methods of order three and four are constructed, which are more effective than functional continuous Runge–Kutta methods of the same order. Numerical tests confirm the convergence order of the new methods. Comparison to closely related Runge–Kutta methods for Volterra integro-differential equations is made. [ABSTRACT FROM AUTHOR]

This paper deals with oscillation of a second order delay differential equation with a nonpositive sublinear neutral term. Some new oscillation criteria are obtained which extend, complement, and correct the results reported in the literature. Also three illustrations are provided to verify our results. [ABSTRACT FROM AUTHOR]

In this paper, we used the modified Adomian Decomposition Method (LADM) joined Padé approximation to solve a system of delay differential equations (DDEs) with initial value problem (IVP). The main objective of the work to solve the Delay differential equations by approximate solutions method. The examples are solved using the presented method and compared the computed result with the exact solution to show the efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented. [ABSTRACT FROM AUTHOR]

We are particularly interested in the numerical solution of the functional differential equations with symmetric delay and advance. In this work, we consider a nonlinear forward-backward equation, the Fitz Hugh-Nagumo equation. It is presented a scheme which extends the algorithm introduced in [1]. A computational method using Newton's method, finite element method and method of steps is developped. [ABSTRACT FROM AUTHOR]

The stability of an inverted pendulum is a textbook example of control. The easiest case is to put the pendulum on a cart and apply feedback force control on it to keep the upright position stable. This paper compares the no delay case (feed-in-time control: an anticipatory effect) and the delay differential equation approach. Then we study both continuous and discrete time systems. The main aim of the work is to investigate the behaviour of such systems at the stability boundaries by using numerical simulation. The principal points of interest are how continuous time systems differ from discrete time system at a bifurcation point and how time delay or an anticipatory feed-in-time control acts on its behaviour. Other exciting questions are how sampling delay can be taken into consideration and is bifurcation a robust phenomenon. [ABSTRACT FROM AUTHOR]

There are different ways of how to model gene regulatory networks. Differential equations allow for a detailed description of the network’s dynamics and provide an explicit model of the gene concentration changes over time. Production and relative degradation rate functions used in such models depend on the vector of steeply sloped threshold functions which characterize the activity of genes. The most popular example of the threshold functions comes from the Boolean network approach, where the threshold functions are given by step functions. The system of differential equations becomes then piecewise linear. The dynamics of this system can be described very easily between the thresholds, but not in the switching domains. For instance this approach fails to analyze stationary points of the system and to define continuous solutions in the switching domains. These problems were studied in [2], [3], but the proposed model did not take into account a time delay in cellular systems. However, analysis of real gene expression data shows a considerable number of time-delayed interactions suggesting that time delay is essential in gene regulation. Therefore, delays may have a great effect on the dynamics of the system presenting one of the critical factors that should be considered in reconstruction of gene regulatory networks. The goal of this work is to apply the singular perturbation analysis to certain systems with delay and to obtain an analog of Tikhonov’s theorem, which provides sufficient conditions for constracting the limit system in the delay case. [ABSTRACT FROM AUTHOR]

Dengue Fever is a dangerous viral disease that is transmitted by female Aedes mosquitoes and is common in more than 100 countries in the world and in all countries of South-East Asia. Mathematical models of Dengue Fever transmission are useful for studying the causes of the spread of the disease and to try to develop methods for reducing the spread of the disease. In this paper, a mathematical model for Dengue fever is analyzed consisting of a system of four nonlinear differential equations with two time delays. The model includes infected humans, infectious humans, infected mosquitoes and infectious mosquitoes. The model has disease-free and endemic equilibrium points. The asymptotic stability of the equilibrium points are studied analytically. The Matlab computer program is used to obtain numerical solutions of the model for both zero and nonzero time delays for a range of parameter values. It is found that for some reasonable estimates of parameter values the endemic equilibrium point is asymptotically stable, but the approach to equilibrium is very slow, suggesting that this equilibrium point may not be of practical importance for these parameter values. Some comparisons are made between the model results and the actual data for Dengue Fever in Thailand, Malaysia and Singapore. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for obtaining explicit solutions for a first order linear delay differential equation with constant coefficients. We conjecture that there is a generating function defined over of a specific class of polynomials in the delay that solves the equation, and prove in the main theorem that the conjecture is valid. We also show the advantage of our method as regards the traditional Method of Step Algorithm (MSA). [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition is obtained for oscillation of bounded solutions of second order impulsive delay differential equations of the form (r(t)x′(t))′ + p(t)f(x(τ(t))) = 0, t ≠ θi, Δ(r(θi)x′(θi)) + big(x(σ(θi))) = 0, i ∈ Z, Δx(θi) = 0. An example is also inserted to illustrate the effect of impulses on the oscillatory behavior of the solutions. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]