Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Qualitative Analysis of Differential Equations: Theory and Applications
share announcement

Special Issue "Qualitative Analysis of Differential Equations: Theory and Applications"

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

Deadline for manuscript submissions: 30 November 2023 | Viewed by 4667

Special Issue Editors

Dr. Osman Tunç

E-Mail Website
Guest Editor
Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Interests: ordinary differential equations; functional differential equations; integro-differential equations; applied mathematics
Prof. Dr. Vitalii Slynko

E-Mail Website
Guest Editor
Institute of Mathematics, University of Wuerzburg, Emil-Fischer-Str., 40, 97074 Wuerzburg, Germany
Interests: zero-solution; Lyapunov function; parabolic systems; switched systems; average dwell time; nonlinear dynamics; fuzzy differential equations; fuzzy numbers; differentiability
Prof. Dr. Sandra Pinelas

E-Mail Website
Guest Editor
Departamento De Ciencias Exatas E Engenharia Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal
Interests: differential equations; difference equations; oscillatory behavior; asymptotic behavior
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the past year, qualitative analyses, i.e., analyses of the stability, boundedness, integrability, existence and uniqueness  of solutions  of functional differential equations (delay differential equations, neutral differential equations, advanced differential equations and  impulsive differential equations); dynamic models; integral equations; integro-differential equations; partial  differential equations; fractional differential equations; fractional integro-differential equations; fractional partial  differential equations; etc., have attracted the attention of numerous researchers at the theoretical level and at the level of their applications. From the relevant literature, it can be observed that numerous processes and problems in biology, the interactions between species, population dynamics, microbiology, distributed networks, mechanics, medicine, nuclear reactors, chemistry, distributed networks, epidemiology, physics, engineering, economics, physiology, viscoelasticity, etc. can be modelled mathematically by these kind of equations.

Therefore, these kind of equations have vital, important roles in real world applications. However, these kind of equations can be solved analytically in particular cases, but not numerically. Qualitative theory can enable us to obtain information about the behaviour of solutions without prior information on them by means of Lyapunov’s second method, the fixed-point method, the Lyapunov–Krasovskii method, and so on. The aim of this SI is to collect some new theoretical contributions and real-world applications with regard to the qualitative theory of  the equations mentioned above. 

Dr. Osman Tunç
Prof. Dr. Vitalii Slynko
Prof. Dr. Sandra Pinelas
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

  • qualitative theory
  • qualitative analysis
  • ordinary differential equations
  • partial differential equations
  • functional differential equations (delay differential equations, neutral differential equations, advanced differential equations, and impulsive differential equations)
  • integral equations
  • integro-differential equations
  • fractional calculus
  • fractional differential equations
  • fractional integral equations
  • fractional integro-differential equations
  • fractional partial differential equations
  • fractional partial integro-differential equations
  • dynamical models of integer orders
  • dynamical models of fractional orders
  • Lyapunov’s second method
  • fixed-point method
  • Lyapunov–Krasovskii method
  • control theory
  • stabilization
  • real-world applications
  • numerical simulations

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

get_app
Article
An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations
by
Osama Moaaz
and
Yousef Alnafisah
Mathematics 2023, 11(10), 2290; https://doi.org/10.3390/math11102290 - 15 May 2023
Viewed by 582
Abstract
In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as well as between the solution and its corresponding [...] Read more.
In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as well as between the solution and its corresponding function, can help to obtain more efficient oscillation criteria for differential equations of neutral type. So, we deduce some new relationships of an iterative nature. Then, we test the effect of these relationships on the criteria that exclude positive solutions to the studied equation. By comparing our results with previous results in the literature, we show the importance and novelty of the new results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
get_app
Article
Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies
by
Azhar Iqbal Kashif Butt
,
Saira Batool
,
Muhammad Imran
and
Muneerah Al Nuwairan
Mathematics 2023, 11(9), 1978; https://doi.org/10.3390/math11091978 - 22 Apr 2023
Cited by 4 | Viewed by 903
Abstract
The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of [...] Read more.
The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new LSHSEAIHR COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, LS, and high-risk susceptible populations, HS. The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model’s most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended LSHSEAIHR model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin’s maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
►▼ Show Figures

Figure 1

get_app
Article
Finite-Element Method for the Simulation of Lipid Vesicle/Fluid Interactions in a Quasi–Newtonian Fluid Flow
by
Aymen Laadhari
Mathematics 2023, 11(8), 1950; https://doi.org/10.3390/math11081950 - 20 Apr 2023
Cited by 1 | Viewed by 595
Abstract
We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty [...] Read more.
We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty which allows computational savings and facilitates implementation. A high-order Galerkin finite element approximation allows accurate calculations of the membrane force with high-order derivatives. The time discretization is based on the double composition of the one-step backward Euler scheme, while the time step size is flexibly controlled using a time integration error estimation. Numerical examples are presented with particular attention paid to the validation and assessment of the model’s relevance in terms of physiological significance. Optimal convergence rates of the time discretization are obtained. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
►▼ Show Figures

Figure 1

get_app
Article
On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application
by
Hasib Khan
,
Jehad Alzabut
,
Haseena Gulzar
,
Osman Tunç
and
Sandra Pinelas
Mathematics 2023, 11(8), 1913; https://doi.org/10.3390/math11081913 - 18 Apr 2023
Cited by 5 | Viewed by 781
Abstract
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order [...] Read more.
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
►▼ Show Figures

Figure 1

get_app
Article
Global Dynamics for Competition between Two Wolbachia Strains with Bidirectional Cytoplasmic Incompatibility
by
Qiming Huang
,
Lijie Chang
,
Zhaowang Zhang
and
Bo Zheng
Mathematics 2023, 11(7), 1691; https://doi.org/10.3390/math11071691 - 01 Apr 2023
Viewed by 565
Abstract
Releasing Wolbachia-infected mosquitoes to suppress or replace wild vector mosquitoes has been carried out in 24 countries worldwide, showing great promise in controlling mosquitoes and mosquito-borne diseases. To face the instability of Wolbachia infection in different environments during the area-wide application, we [...] Read more.
Releasing Wolbachia-infected mosquitoes to suppress or replace wild vector mosquitoes has been carried out in 24 countries worldwide, showing great promise in controlling mosquitoes and mosquito-borne diseases. To face the instability of Wolbachia infection in different environments during the area-wide application, we should consider the overlapping of two Wolbachia strains. In this case, bidirectional cytoplasmic incompatibility occurs, which results in mating partners infected with exclusive Wolbachia strains producing inviable offspring. To determine the better Wolbachia candidate for release, we develop an ordinary differential equation model to study the global dynamics for competition between two Wolbachia strains. Our theoretical results on the sharp estimate of stable curves completely determine the fate of the two Wolbachia strains, which help choose appropriate strains for release. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
►▼ Show Figures

Figure 1

get_app
Article
Oscillatory Properties of Fourth-Order Advanced Differential Equations
by
Alanoud Almutairi
,
Ali Hasan Ali
,
Omar Bazighifan
and
Loredana Florentina Iambor
Mathematics 2023, 11(6), 1391; https://doi.org/10.3390/math11061391 - 13 Mar 2023
Viewed by 562
Abstract
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding [...] Read more.
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding of fourth-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop