Nonlinear delay differential equations and their application to modeling biological network motifs by David S. Glass, Xiaofan Jin, Ingmar H. Riedel-Kruse

“…Here, the authors systematically examine the most common network motifs via delay differential equations (DDE), often leading to more concise descriptions.…”
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New Comparison Results for Oscillation of Even-Order Delay Differential Equations by Barakah Almarri, Fahd Masood, Ali Muhib, Osama Moaaz

Subjects: “…delay differential equations…”
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Existence, uniqueness, and stability of uncertain delay differential equations with V-jump by Zhifu Jia, Xinsheng Liu, Cunlin Li

“…Abstract No previous study has involved uncertain delay differential equations with jump. In this paper, we consider the uncertain delay differential equations with V-jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. …”
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Numerical Treatment of Delay-Differential Equations by Using Spline Hermite Approximations by Suliman Mahmoud, Mohamad Ali, Bashar Gdeed

“… In this paper, spline technique with five collocation parameters for finding the numerical solutions of delay differential equations (DDEs) is introduced. The presented method is based on the approximating the exact solution by C4-Hermite spline interpolation and as well as five collocation points at every subinterval of DDE.The study shows that the spline solution of purposed technique is existent and unique and has strongly stable for some collocation parameters. …”
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On the Oscillatory Properties of Solutions of Second-Order Damped Delay Differential Equations by Awatif A. Hendi, Osama Moaaz, Clemente Cesarano, Wedad R. Alharbi, Mohamed A. Abdou

“…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 to apply. …”
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Oscillation theorems for fourth-order quasi-linear delay differential equations by Fahd Masood, Osama Moaaz, Shyam Sundar Santra, U. Fernandez-Gamiz, Hamdy A. El-Metwally

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scillation criteria for first-order nonlinear neutral delay differential equations by Elmetwally M. Elabbasy, Taher S. Hassan, Samir H. Saker

“…Oscillation criteria are obtained for all solutions of first-order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature. …”
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Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform by Reem Alrebdi, Hind K. Al-Jeaid

“…The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics. …”
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Oscillation of second-order Emden-Fowler neutral delay differential equations by Yingzhu Wu, Yuanhong Yu, Jinsen Xiao

“…In this article, we establish new oscillation criteria for the second-order Emden-Fowler neutral delay differential equation $$ \Big(r(t)|z'(t)|^{\alpha-1}z'(t)\Big)'+q(t)|x(\sigma(t))|^{\beta-1} x\big(\sigma(t)\big)=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)), \alpha>0$ and $\beta>0$. …”
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Behavior of the solutions to second order linear autonomous delay differential equations by Ioannis K. Purnaras, Christos G. Philos

Subjects: “…Delay differential equation…”
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Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate by Lokesh Singh, Dhirendra Bahuguna

Subjects: “…delay differential equation…”
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Oscillatory behavior of solutions of odd-order nonlinear delay differential equations by Osama Moaaz

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Existence of unstable manifolds for a certain class of delay differential equations by Hari P. Krishnan

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Sharp results for oscillation of second-order neutral delay differential equations by Martin Bohner, Said Grace, Irena Jadlovská

“…The aim of the present paper is to continue earlier works by the authors on the oscillation problem of second-order half-linear neutral delay differential equations. By revising the set method, we present new oscillation criteria which essentially improve a number of related ones from the literature. …”
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On the qualitative behavior of the solutions to second-order neutral delay differential equations by Shyam Sundar Santra, Hammad Alotaibi, Omar Bazighifan

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Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations by Blanka Baculíková, Jozef Džurina

“…We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation \begin{equation*} \left(r(t)\left[x'(t)\right]^{\gamma}\right)^{(n-1)}+q(t)x^{\gamma}(\tau(t))=0.…”
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Analysis of stochastic delay differential equations in the framework of conformable fractional derivatives by Muhammad Imran Liaqat, Fahim Ud Din, Wedad Albalawi, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty

Subjects: “…conformable fractional stochastic delay differential equations…”
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Approximate controllability of nonautonomous nonlocal delay differential equations with deviating arguments by Rajib Haloi

“…The objective of this article is to prove sufficient conditions for the approximate controllability for a class of nonautonomous nonlocal finite delay differential equations with deviating arguments in a Hilbert space. …”
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Delay differential equations and the dose-time dependence of early radiotherapy reactions. by Fenwick, J

“…Several formulas have been derived from the delay differential equation, predicting changes in isoeffective total radiation dose with schedule duration for different types of fractionation scheme. …”

Hybrid multistep block method for solving neutral delay differential equations by Nur Inshirah Naqiah Ismail, Zanariah Abdul Majid, Norazak Senu

“…The initial-value problem for first order single linear neutral delay differential equations (NDDEs) of constant and pantograph delay types have been solved by using hybrid multistep block method. …”
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