Search · four archives
Search · four archives
20 papers · ranked by Valyu relevance
Hamid Bounit, A. Driouich, Saïd Hadd
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish their existence and uniqueness, under suitable assumptions. Furthermore, we…
Kenta Nakata, Ken‐ichi Maruno
We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions. It is carried out by applying a reduction and delay-differential limit to the…
В. А. Дородницын, Roman S. Kozlov, Sergey V. Meleshko
We review studies on the application of Lie group methods to delay ordinary differential equations (DODEs). For first- and second-order DODEs with a single delay parameter that depends on independent and dependent variables, the group classifications are performed. Classes of invariant DODEs for each Lie subgroup are…
Sachin Bhalekar, Deepa Gupta
one can have a critical value of α viz α∗ such that the system is stable for 0 < α < α∗ and unstable for α∗ < α ≤ 1. In general, if such system is stable for some α0 ∈ (0, 1) then it remains stable for all α < α0.
Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc + 1 more
'V. Govindaraj'] We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point…
В. А. Дородницын, R. V. Kozlov, Sergey V. Meleshko
A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance of a Lagrangian function with the appropriate variational equations and the conserved quantities. The identity is used to…
Gemeda Tolessa Lubo, Gemechis File Duressa
Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that…
Chavda Divyesh Vinodbhai, Shruti Dubey
In this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays. The method is implemented by replacing the hidden layer of the feed-forward neural network with the orthogonal…
Ababi Hailu Ejere, Gemechis File Duressa, Mesfin Mekuria Woldaregay, Tekle Gemechu Dinka
'Tekle Gemechu Dinka'] In this study, a parameter-uniform numerical scheme is built and analyzed to treat a singularly perturbed parabolic differential equation involving large spatial delay. The solution of the considered problem has two strong boundary layers due to the effect of the perturbation parameter, and the…
H. A. A. El-Saka, D. El. A. El-Sherbeny, A. M. A. El-Sayed
In this paper, we analyze the stability of the fractional distributed delay models. We use the linear chain trick to convert these models into an incommensurate fractional order systems. We get the stability regions by studying the characteristic equation around equilibrium points. We investigate how the fractional…
A.V. Paraskevov
Starting with the classical biophysical Morris-Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the…
В. А. Дородницын, Roman Kozlov, Sergey V. Meleshko
a Keldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl. 4, Moscow, 125047, Russia; e-mail: Dorodnitsyn@Keldysh.ru, dorod2007@gmail.com b Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, 5045, Bergen, Norway; e-mail: Roman.Kozlov@nhh.no c School…
Christopher N. Angstmann, Stuart-James M. Burney, Daniel Han, B. I. Henry + 1 more
'B. I. Henry' 'Zhijie Xu'] Exact solutions are derived for a time-delay advection equation and a fractional-order time-delay advection equation with a time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a…
Vivi Andasari, S. Syafiie
Cell migration, both in vivo and in vitro, is a complex process governed by mechano-chemical interactions between cells and the extracellular matrix (ECM). These interactions, mediated by cell membrane receptors called integrins, involve bidirectional signaling between the intracellular actin cytoskeleton and the ECM.…
Ababi Hailu Ejere, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay, Gemechis File Duressa
'Gemechis File Duressa'] Objective The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the…
Zahra Sadat Aghayan, Alireza Alfi, António M. Lopes, Vasily E. Tarasov
'Vasily E. Tarasov'] In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional-differential output feedback controller to obtain a satisfactory…
Jacek Miȩkisz, Javad Mohamadichamgavi, Raffi Vardanyan
We present a microscopic model of replicator dynamics with strategy-dependent time delays. In such a model, new players are born from parents who interacted and received payoffs in the past. In the case of small delays, we use Taylor expansion to get ordinary differential equations for frequencies of strategies with…
Quanmin Zhu, Jianhua Zhang, Weicun Zhang, José María Amigó
This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
Dipali Vasudev Mestry, Pratik Singh, Joacim Rocklöv, Amiya Ranjan Bhowmick
The evolution of eco-epidemiological systems is significantly influenced by the memory or previous history of the system. These non-Markovian dynamics are effectively modelled using fractional derivatives (FDs), incorporating memory kernels that reflect long-term or short-term memory characteristics in corresponding…