709 Results Found

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

Uncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differentia...

The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces $\mathcal{R}([-r,0],{\mathbb{R}}^n).$ The existence of the periodic solution of impulsiv...

This article discusses several forms of Ulam stability of nonlinear fractional delay differential equations. Our investigation is based on a generalised Gronwall’s inequality and Picard operator theory. Implementations are provided to demonstra...

Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms. At the moment, only a few low-order algorithms offer acceptabl...

Stochastic robustness of discrete noises has already been proposed and studied in the previous work. Nevertheless, the significant phenomenon of delays is left in the basket both in the deterministic and the stochastic parts of the considered equatio...

In this paper, neutral delay differential equations, which contain constant and proportional terms, termed mixed neutral delay differential equations, are solved numerically. Moreover, an efficient numerical approach is introduced (a combination of t...

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coeffic...

In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscil...

This paper explores the linearized stability of nonlinear delay differential equations (DDEs) with impulses. The classical results on the existence of periodic solutions are extended from ordinary differential equations (ODEs) to DDEs with impulses....

The purpose of this paper is to give new oscillation criteria for second-order delay differential equations $y^{″}\left(t\right)=p\left(t\right)y\left(\tau \left(t\right)\right).$ We introduce a new technique for the elimination of bounded nonoscillatory solutions.

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 co...

This paper examines solutions to mathematical models based on functional-differential equations, which have applications in immunology. This new approach allows us to study discontinuous solutions that more accurately depict real-world phenomena. It...

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, the existence and uniqueness theorem of a solution for the delay integro-differential equation is obtained using a Lipschitz condition and the B...

In this paper, we study a class of second-order delay fractional differential equations with a variable-order Caputo derivative. This type of equation is an extension to ordinary delay equations which are used in the modeling of several biological sy...

As an important mathematical model actuated by the Liu process, uncertain delay differential equations depict the development of system dynamics. In the applications of uncertain delay differential equations, parameter estimation plays a key role. In...

This paper concerns the existence and precise expression form of entire solutions to a certain type of delay-differential equation. The significance of our results lie in that we generalize and supplement the related results obtained recently.

Variational iteration method is applied to solve a class of delay differential-algebraic equations. The obtained sequence of iteration is based on the use of Lagrange multipliers. The corresponding convergence results are obtained and successfully co...

We consider a class of second-order nonlinear delay differential equations with periodic coefficients in linear terms. We obtain conditions under which the zero solution is asymptotically stable. Estimates for attraction sets and decay rates of solut...

We study first order linear impulsive delay differential equations with periodic coefficients and constant delays. This study presents some new results on the asymptotic behavior and stability. Thus, a proper real root was used for a representative c...

In this article, we study some existence and controllability results for two classes of second order functional differential equations with delay and random effects. To begin, we employ a random fixed point theorem with a stochastic domain to demonst...

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theo...

Delay-differential equations belong to the class of infinite-dimensional dynamical systems. However, it is often observed that the solutions are rapidly attracted to smooth manifolds embedded in the finite-dimensional state space, called inertial man...

In this paper, effective oscillation criteria for third-order delay differential equations of the form, ${\left(r_2{\left(r_1{y}^{\prime }\right)}^{\prime }\right)}^{\prime }\left(t\right)+q\left(t\right)y\left(\tau \left(t\right)\right)=0$ ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when a...

Let X be a Banach space, $A:D(A)\subset X\to X$ the generator of a compact $C_0$ -semigroup $S(t):X\to X,t\ge 0$ , $D(·):(a,b)\to 2^X$ a tube in X, and $f:(a,b)\times \mathcal{B}\to X$ a function of Carathéodory t...

The present study aims to integrate the Adomian decomposition method with the Sumudu transform for solving delay fractional partial differential equations. Integrating these two methods enhances accuracy and computational efficiency, providing an eff...

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and se...

In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We...

We present a new method for obtaining stability conditions for certain classes of delay differential equations. The method is based on the transition from an individual equation to a family of equations, and next the selection of a representative of...

In this article, we study a class of non-linear neutral delay differential equations of third order. We first prove criteria for non-existence of non-Kneser solutions, and criteria for non-existence of Kneser solutions. We then use these results to p...

In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the...

Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimate...

In this paper, we obtain new monotonic properties for positive solutions of even-order delay differential equations in the non-canonical case. Using these properties, we establish a new oscillation criterion for solutions by comparison with an equati...

It is known that the method of Lyapunov functionals is a powerful method of stability investigation for functional differential equations. Here, it is shown how the previously proposed method of stability investigation for nonlinear stochastic differ...

In this article, we consider a delayed system of first-order hyperbolic differential equations. The presence of the delay term in first-order hyperbolic delay differential equations poses significant challenges in both analysis and numerical solution...

In this study, new asymptotic properties of positive solutions of the even-order delay differential equation with the noncanonical operator are established. The new properties are of an iterative nature, which allows it to be applied several times. M...

In this work, we adopted an approach similar to that of Chatzarakis’, by transforming the oscillation analysis of third-order differential equations into an equivalent first-order problem. A key generalization in our study is the extension coef...

In the present paper, a fifth-order direct multistep block method is proposed for solving the second-order Delay Differential Equations (DDEs) directly with boundary conditions using constant step size. In many life sciences applications, a delay pla...

In the current contribution, integral representations of the solutions of homogeneous and nonhomogeneous delay differential equation of a fractional Hilfer derivative are established in terms of the delayed Mittag-Leffler-type matrix function of two...

This paper is concerned with collocation methods for one class of impulsive delay differential equations (IDDEs). Some results for the convergence, global superconvergence and local superconvergence of collocation methods are given. We choose a suita...

In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. Natural transform decompositio...

New oscillatory properties for the oscillation of solutions to a class of fourth-order delay differential equations with several deviating arguments are established, which extend and generalize related results in previous studies. Some oscillation re...

The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This d...

In the work, a new oscillation condition was created for second-order damped delay differential equations with a non-canonical operator. The new criterion is of an iterative nature which helps to apply it even when the previous relevant results fail...

The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differentia...

In this paper, first, we give a definition of Besicovitch almost periodic functions by using the Bohr property and the Bochner property, respectively; study some basic properties of Besicovitch almost periodic functions, including composition theorem...

This paper presents the idea of the Sawi iterative scheme (SIS) to derive the analytical solution of nonlinear delay differential equations (DDEqs). We apply the Sawi transform to construct a recurrence relation which is now easy to handle and the im...

In this paper, we investigate the representation of solution for the following linear matrix delayed differential equation $\dot{Y}\left(t\right)=A_{1}Y\left(t\right)+Y\left(t\right)A_2+BY(t-\tau )+Y(t-\tau )C+F\left(t\right),t\in [0,\infty )$ where t is an independent variable, $Y\left(t\right)$ i...

Mathematical models have been of great importance in various fields, especially for understanding the dynamical behaviour of biosystems. Several models, based on classical ordinary differential equations, delay differential equations, and stochastic...

This article presents several key findings for fractional-order delay differential equations. First, we establish the existence and uniqueness of solutions using two distinct approaches, the Chebyshev norm and the Bielecki norm, thereby providing a c...