Time delay and noise explaining the behaviour of the cell growth in fermentation process by Ayuobi, Tawfiqullah, Rosli, Norhayati, Bahar, Arifah, Md. Salleh, Madihah

“…Time delay and noise are modelled jointly via stochastic delay differential equations (SDDEs). The typical behaviour of cell concentration in batch fermentation process under this model is investigated. …”

Besicovitch Almost Periodic Solutions of Abstract Semi-Linear Differential Equations with Delay by Yongkun Li, Mei Huang, Bing Li

“…Then, using the contraction fixed point theorem, we study the existence and uniqueness of Besicovitch almost periodic solutions for a class of abstract semi-linear delay differential equations. Even if the equation we consider degenerates into ordinary differential equations, our result is new.…”
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Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems by Ravi Agarwal, Snezhana Hristova, Donal O’Regan

“…First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. …”
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New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms by Shyam Sundar Santra, Omar Bazighifan, Mihai Postolache

“…In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. …”
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New Fundamental Results on the Continuous and Discrete Integro-Differential Equations by Osman Tunç, Cemil Tunç, Jen-Chih Yao, Ching-Feng Wen

“…This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. …”
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Discrete and Differential Equations in Applied Mathematics by Miroslava Ruzickova

“…We illustrate some results from control theory for discrete delayed equations, perturbed linear problems for discrete equations, results concerning the structure of solutions of delayed differential equations, results of orthogonal polynomials, and adescription of some numerical investigations in discrete least-squares and collocation methods for numerical solution of a boundary value and eigenvalue problems. …”
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Analysis of a nonlinear problem involving discrete and proportional delay with application to Houseflies model by Kamal Shah, Muhammad Sher, Muhammad Sarwar, Thabet Abdeljawad

“…This manuscript established a comprehensive analysis of a general class of fractional order delay differential equations with Caputo-Fabrizio fractional derivative (CFFD). …”
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Synchronization in coupled Ikeda delay system by Valli, D., Muthuswamy, Bharathwaj, Banerjee, Santo, Kamel Ariffin, Muhammad Rezal, Abdul Wahab, Ainuddin Wahid, Kaliyaperumal, Ganesan, Subramaniam, Chittur Krishnaswamy, Kurths, Juergen

“…In this work, we demonstrate the use of a Field Programmable Gate Array (FPGA) as a physical platform for realizing chaotic delay differential equations (DDE). Moreover, using our platform, we also experimentally study the synchronization between two time delayed systems. …”

On a study of the representation of solutions of a Ψ-Caputo fractional differential equations with a single delay by Mustafa Aydin, Nazim I. Mahmudov, Hüseyin Aktuğlu, Erdem Baytunç, Mehmet S. Atamert

“…We give a representation of solutions to linear nonhomogeneous Ψ-fractional delayed differential equations with noncommutative matrices. We newly define Ψ-delay perturbation of Mittag-Leffler type matrix function with two parameters and apply the method of variation of constants to obtain the representation of the solutions. …”
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The controllability of nonlinear fractional differential system with pure delay by Musarrat Nawaz, Wei Jiang, Jiale Sheng

“…The solution representations of fractional delay differential equations have been established by using the delayed Mittag-Leffler function. …”
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Solución Uniformemente Acotada y Estabilidad Asintótica del Punto Libre de Infección de un Modelo Matemático SI con Dinámica Vital (crecimiento logístico) mediante las Ecuaciones D... by Neisser Pino Romero, Christian Ulises Salazar Fernández, Roxana López Cruz

“…In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. …”
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Mathematical Model of Antiviral Immune Response against the COVID-19 Virus by Juan Carlos Chimal-Eguia

“…We built a mathematical model of delay differential equations describing a simplified view of the mechanism between the COVID-19 virus infection and the immune system. …”
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Some asymptotic properties of SEIRS models with nonlinear incidence and random delays by Divine Wanduku, B.O. Oluyede

“…The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. …”
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Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment by A. M. Elaiw, A. A. Raezah, S. A. Azoz

“…We solve the system of delay differential equations numerically to support the theoretical results.…”
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Stability of latent pathogen infection model with CTL immune response and saturated cellular infection by A. M. Elaiw, A. A. Almatrafi, A. D. Hobiny, I. A. Abbas

“…We solve the system of delay differential equations numerically to support the theoretical results.…”
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On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments by Muminov, M. I.

“…This paper provides a method of finding periodical solutions of the second-order neutral delay differential equations with piecewise constant arguments of the form x″(t)+px″(t−1)=qx(2[t+12])+f(t), where [ ⋅ ] denotes the greatest integer function, p and q are nonzero constants, and f is a periodic function of t. …”
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Asymptotic methods for delay equations by Fowler, A

“…Asymptotic methods for singularly perturbed delay differential equations are in many ways more challenging to implement than for ordinary differential equations. …”

Global dynamics of a two-strain HIV infection model with intracellular delay by Jin Xu

“…Model is in the form of a delay differential equations with a two discrete delays to account for the average time for replication for the two strains. …”
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On Pseudo Almost Automorphic Solutions to Quaternion-Valued Cellular Neural Networks With Delays by Changjin Xu

“…Applying pseudo almost automorphic solution theory of delayed differential equations and pertinent inequalities, a new sufficient criterion to guarantee the existence and global exponentially stability of pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays are presented. …”
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Global Hopf bifurcation of a delayed phytoplankton-zooplankton system considering toxin producing effect and delay dependent coefficient by Zhichao Jiang, Xiaohua Bi, Tongqian Zhang, B.G. Sampath Aruna Pradeep

“…Firstly, it gives the nonnegative and boundedness of solutions of the delay differential equations. Secondly, it gives the asymptotical stability properties of equilibria in the absence of time delay. …”
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