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Special Issue "Functional Differential Equations: Theory and Applications–Dedicated to the Memory of Nikolay V. Azbelev on the Occasion of His 100th Birthday Anniversary"

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 October 2023 | Viewed by 2832

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Prof. Dr. Vladimir P. Maksimov

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Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990 Perm, Russia
Interests: functional differential equations with ordinary derivatives; continuous-discrete systems with aftereffect; boundary value problems, control problems; attainability sets; reliable computing experiment in the study of linear problems; economic dynamics models
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Alexander Domoshnitsky

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Department of Mathematics, Ariel University, Ariel 40700, Israel
Interests: functional differential equations; general theory; boundary value problems; positivity of solutions; nonoscillation; distances between adjacent zeros of solutions; distribution of zeros; Sturm’s theorem; stability; feedback control; delay differential equations; integro-differential equations; impulsive equations; applications of equations with memory in technology and medicine
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Issue is dedicated to the memory of Professor Nikolay Azbelev on the occasion of his 100^th birthday anniversary.

Professor N. Azbelev, a well-known Russian mathematician, has been a leading figure in the integral and functional differential equations profession for about five decades. He is one of creators of the contemporary Theory of Functional Differential Equations. Today, this theory is being developed by the efforts of researchers from many countries in order to find more relevant applications.

The key idea of the Issue is to present new high-quality results in all major sections of the theory and in its applications. The topic of the Issue covers the following sections of the theory, but is not limited to them: general theory, boundary value problems, control problems, stability, asymptotic properties of solutions, oscillation/non-oscillation, numerical methods, and reliable computing.

Prof. Dr. Vladimir P. Maksimov
Prof. Dr. Alexander Domoshnitsky
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

functional differential equations
general theory
boundary value problems
control problems
stability
asymptotic properties of solutions
oscillation/non-oscillation
numerical methods and reliable computing
applied problems

Published Papers (4 papers)

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Research

Open AccessArticle

Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay

Vladimir Pimenov

and

Andrei Lekomtsev

Mathematics 2023, 11(18), 3941; https://doi.org/10.3390/math11183941 - 16 Sep 2023

Viewed by 266

Abstract

For a space-fractional diffusion equation with a nonlinear superdiffusion coefficient and with the presence of a delay effect, the grid numerical method is constructed. Interpolation and extrapolation procedures are used to account for the functional delay. At each time step, the algorithm reduces to solving a linear system with a main matrix that has diagonal dominance. The convergence of the method in the maximum norm is proved. The results of numerical experiments with constant and variable delays are presented. Full article

(This article belongs to the Special Issue Functional Differential Equations: Theory and Applications–Dedicated to the Memory of Nikolay V. Azbelev on the Occasion of His 100th Birthday Anniversary)

Open AccessArticle

Mathematical Modeling of COVID-19 Transmission in the Form of System of Integro-Differential Equations

Alexander Domoshnitsky

Alexander Sitkin

and

Lea Zuckerman

Mathematics 2022, 10(23), 4500; https://doi.org/10.3390/math10234500 - 29 Nov 2022

Viewed by 674

Abstract

The model of the spread of the coronavirus pandemic in the form of a system of integro-differential equations is studied. We focus our consideration on the number of hospitalized patients, i.e., on the needs of the system regarding hospital beds that can be provided for hospitalization and the corresponding medical personnel. Traditionally, in such models, the number of places needed was defined as a certain percentage of the number of infected at the moment. This is not quite adequate, since it takes a certain period of time for the development of the disease to the stage at which hospitalization is required. This will be especially evident at the start of new waves of the epidemic, when there is a large surge in the number of infected people, but the need for hospitalization places and additional medical personnel will appear later. Taking this circumstance into account using integral terms in the model allows us to conclude in corresponding additional to existing cases that the wave of disease will attenuate after some time. In others, it will relieve unnecessary panic, because the healthcare system has a certain period to create additional hospitalization places, order medicines and mobilize the necessary medical personnel. We obtain estimates of reproduction number in the case of the model described by a system of integro-differential equations. Results on the exponential stability of this integro-differential system are obtained. It is demonstrated that the condition of the exponential stability coincides with the fact that the reproduction number of the spread of the pandemic is less than one. Full article

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Open AccessArticle

On the Optimal Control Problem for Vibrations of the Rod/String Consisting of Two Non-Homogeneous Sections with the Condition at an Intermediate Time

Vanya Barseghyan

and

Svetlana Solodusha

Mathematics 2022, 10(23), 4444; https://doi.org/10.3390/math10234444 - 24 Nov 2022

Viewed by 620

Abstract

We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The wave equation describes the longitudinal vibrations of a non-homogeneous rod or the transverse vibrations of a non-homogeneous string with given initial, intermediate, and final conditions. We assume that wave travel time for each of the sections is the same. The control is carried out by shifting one end with the other end fixed. The quality criterion is set on the entire time interval. A constructive approach to building an optimal boundary control is proposed. The results obtained are illustrated with an analytical example. Full article

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Open AccessFeature PaperArticle

Negativity of Green’s Functions to Focal and Two-Point Boundary Value Problems for Equations of Second Order with Delay and Impulses in Their Derivatives

Alexander Domoshnitsky

Sergey Malev

and

Vladimir Raichik

Mathematics 2022, 10(19), 3683; https://doi.org/10.3390/math10193683 - 08 Oct 2022

Viewed by 713

Abstract

We consider the second-order impulsive differential equation with impulses in derivative and without the damping term. Sufficient conditions that a nontrivial solution of the homogeneous equation having a zero of its derivative does not have a zero itself are obtained. On the basis of the obtained results on differential inequalities, which can be considered as analogues of the Vallee–Poussin theorems, new sufficient conditions on the negativity of Green’s functions are obtained. Full article

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Special Issue "Functional Differential Equations: Theory and Applications–Dedicated to the Memory of Nikolay V. Azbelev on the Occasion of His 100th Birthday Anniversary"

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