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Mathematics
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The Theory of Differential Equations and Their Applications
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The Theory of Differential Equations and Their Applications

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

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 4757

Special Issue Editors

Prof. Xiping Liu

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Guest Editor
Department of Mathematics, College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Interests: fractional differential equations; functional differential equations
Prof. Dr. Liu Yang

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Guest Editor
Department of Mathematics and Statistics, Hefei Normal University, Hefei 230001, China
Interests: nonlinear differential equation
Dr. Ruiyang Cai

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Guest Editor
Department of Mathematics, College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Interests: fractional differential equations; control theory of fractional ordinary/partial differential equations; stability analysis

Special Issue Information

Dear Colleagues,

Differential equations are one of the core areas of analytical mathematics, playing a fundamental role in modern science and practical engineering. With the promotion of science and technology, in recent years, the theory of differential equations and its applications have rapidly developed, and new waves have been successively set off in these research fields.

The aim of this Special Issue is to attract original frontier contributions on the theory of fractional differential equations and functional differential equations, including but not limited to initial value problems, boundary value problems, qualitative theory, stability analysis, control theory and numerical solutions. Moreover, we encourage submissions of their applications in bioscience, economy, information engineering, and so on.

Prof. Xiping Liu
Prof. Dr. Liu Yang
Dr. Ruiyang Cai
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

  • fractional differential equations
  • functional differential equations
  • boundary value problems
  • qualitative theory
  • stability analysis
  • control theory

Published Papers (6 papers)

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Research

19 pages, 336 KiB  
Article
A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics
by Manuel De la Sen
Mathematics 2024, 12(7), 960; https://doi.org/10.3390/math12070960 - 24 Mar 2024
Viewed by 543
Abstract
This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a [...] Read more.
This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
18 pages, 602 KiB  
Article
Stability Analysis of a Delayed Paranthrene tabaniformis (Rott.) Control Model for Poplar Forests in China
by Meiyan Wang, Leilei Han and Yuting Ding
Mathematics 2024, 12(6), 827; https://doi.org/10.3390/math12060827 - 12 Mar 2024
Viewed by 531
Abstract
Forest pests and diseases can diminish forest biodiversity, damage forest ecosystem functions, and have an impact on water conservation. Therefore, it is necessary to analyze the interaction mechanism between plants and pests. In this paper, the prevention and control of a specific pest—namely [...] Read more.
Forest pests and diseases can diminish forest biodiversity, damage forest ecosystem functions, and have an impact on water conservation. Therefore, it is necessary to analyze the interaction mechanism between plants and pests. In this paper, the prevention and control of a specific pest—namely the larva of Paranthrene tabaniformis (Rott.) (hereinafter referred to as larva)—are studied. Based on the invasion mechanism of the larva in poplar, we establish a delayed differential equation and analyze the existence and stability of equilibria. Next, we assess the existence of a Hopf bifurcation to determine the range of parameters that ensures that the equilibria are stable. Then, we select a set of parameters to verify the results of the stability analysis. Finally, we provide biological explanations and effective theoretical control methods for poplar pests and diseases. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
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13 pages, 285 KiB  
Article
New Criteria for Oscillation of Advanced Noncanonical Nonlinear Dynamic Equations
by Taher S. Hassan, Rami Ahmad El-Nabulsi, Naveed Iqbal and Amir Abdel Menaem
Mathematics 2024, 12(6), 824; https://doi.org/10.3390/math12060824 - 12 Mar 2024
Cited by 1 | Viewed by 624
Abstract
In this study, novel criteria are derived to ensure the oscillation of solutions in nonlinear advanced noncanonical dynamic equations. The obtained results are reminiscent of the criteria proposed by Hille and Ohriska for canonical dynamic equations. Additionally, this paper addresses a previously unresolved [...] Read more.
In this study, novel criteria are derived to ensure the oscillation of solutions in nonlinear advanced noncanonical dynamic equations. The obtained results are reminiscent of the criteria proposed by Hille and Ohriska for canonical dynamic equations. Additionally, this paper addresses a previously unresolved issue found in numerous existing works in the literature on advanced dynamic equations. This study provides a range of illustrative examples to showcase the precision, practicality, and adaptability of the obtained findings. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
23 pages, 353 KiB  
Article
Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p-Laplacian-like Operators and Neutral Delay Arguments
by Mansour Alatwi, Osama Moaaz, Wedad Albalawi, Fahd Masood and Hamdy El-Metwally
Mathematics 2024, 12(3), 470; https://doi.org/10.3390/math12030470 - 1 Feb 2024
Viewed by 717
Abstract
This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their [...] Read more.
This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
12 pages, 274 KiB  
Article
Oscillation of Third-Order Differential Equations with Advanced Arguments
by Munirah Aldiaiji, Belgees Qaraad, Loredana Florentina Iambor, Safi S. Rabie and Elmetwally M. Elabbasy
Mathematics 2024, 12(1), 93; https://doi.org/10.3390/math12010093 - 27 Dec 2023
Cited by 1 | Viewed by 796
Abstract
The main objective of this work was to study some oscillatory and asymptotic properties of a new class of advanced neutral differential equations. Using new relations to link the solution and its corresponding function, we introduced new oscillatory criteria that aim to enhance, [...] Read more.
The main objective of this work was to study some oscillatory and asymptotic properties of a new class of advanced neutral differential equations. Using new relations to link the solution and its corresponding function, we introduced new oscillatory criteria that aim to enhance, simplify, and complement some of current results. We provide some examples to demonstrate the significance of our results. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
15 pages, 321 KiB  
Article
Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior
by Asma Al-Jaser, Belgees Qaraad, Omar Bazighifan and Loredana Florentina Iambor
Mathematics 2023, 11(12), 2605; https://doi.org/10.3390/math11122605 - 7 Jun 2023
Cited by 3 | Viewed by 780
Abstract
In this paper, new criteria for a class oscillation of second-order delay differential equations with distributed deviating arguments were established. Our method mainly depends on making sharper estimates for the non-oscillatory solutions of the studied equation. By using the Ricati technique and comparison [...] Read more.
In this paper, new criteria for a class oscillation of second-order delay differential equations with distributed deviating arguments were established. Our method mainly depends on making sharper estimates for the non-oscillatory solutions of the studied equation. By using the Ricati technique and comparison theorems that compare the studied equations with first-order delay differential equations, we obtained new and less restrictive conditions that ensure the oscillation of all solutions of the studied equation. Further, we give an illustrative example. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
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