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Symmetry
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Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ
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Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 14133

Special Issue Editor

Dr. Omar Bazighifan

E-Mail Website
Guest Editor
1. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
2. Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
Interests: qualitative theory; ordinary differential equations; functional differential equations; dynamical systems; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Neutral differential equations (NDEs) are differential equations with delays, where the delays can appear in both the state variables and their time derivatives.

Ordinary and partial differential equations are universally recognized as powerful tools to model and solve practical problems involving nonlinear phenomena. In particular, we mention physical processes as problems in elasticity theory, where we deal with composites made of two different materials with different hardening exponents.

Therefore, the theory of differential equations has been successfully applied to establish the existence and multiplicity of solutions of boundary value problems via direct methods, minimax theorems, variational methods, and topological methods. If possible, one looks towards solutions in special forms by using the symmetries of the driving equation. This also leads to the study of the difference counterparts of such equations to provide exact or approximate solutions. We mention the reduction methods for establishing exact solutions as solutions of lower-dimensional equations.

This Special Issue will accept high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology.

Dr. Omar Bazighifan
Guest Editor

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • symmetry operators
  • mathematical modeling techniques
  • qualitative properties of solutions
  • oscillation theory
  • delay differential equations
  • ordinary differential/ difference equations
  • partial/functional equations
  • fractional differential and integral calculus
  • applications
 

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Published Papers (8 papers)

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Research

13 pages, 269 KiB  
Article
Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations
by Taher S. Hassan, Loredana Florentina Iambor, Sorin Mureşan, Khalid Alenzi, Ismoil Odinaev and Khudhayr A. Rashedi
Symmetry 2024, 16(9), 1156; https://doi.org/10.3390/sym16091156 - 5 Sep 2024
Viewed by 803
Abstract
This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings [...] Read more.
This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
13 pages, 2982 KiB  
Article
Stability Analysis of the Solution for the Mixed Integral Equation with Symmetric Kernel in Position and Time with Its Applications
by Faizah M. Alharbi
Symmetry 2024, 16(8), 1048; https://doi.org/10.3390/sym16081048 - 14 Aug 2024
Viewed by 502
Abstract
Under certain assumptions, the existence of a unique solution of mixed integral equation (MIE) of the second type with a symmetric kernel is discussed, in L2[Ω]×C0,T,T<1,Ω is the [...] Read more.
Under certain assumptions, the existence of a unique solution of mixed integral equation (MIE) of the second type with a symmetric kernel is discussed, in L2[Ω]×C0,T,T<1,Ω is the position domain of integration and T is the time. The convergence error and the stability error are considered. Then, after using the separation technique, the MIE transforms into a system of Hammerstein integral equations (SHIEs) with time-varying coefficients. The nonlinear algebraic system (NAS) is obtained after using the degenerate method. New and special cases are derived from this work. Moreover, numerical results are computed using MATLAB R2023a software. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
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16 pages, 285 KiB  
Article
New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations
by Asma Al-Jaser, Belgees Qaraad, Faizah Alharbi and Stefano Serra-Capizzano
Symmetry 2024, 16(7), 817; https://doi.org/10.3390/sym16070817 - 29 Jun 2024
Viewed by 637
Abstract
The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for [...] Read more.
The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for testing whether the studied equation exhibits oscillatory behavior or converges to zero. Our results contribute uniquely to oscillation theory by presenting some theorems that improve and expand upon the results found in the existing literature. We also provide an example to corroborate the validity of our proposed criteria. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
27 pages, 5606 KiB  
Article
New Numerical Methods for Solving the Initial Value Problem Based on a Symmetrical Quadrature Integration Formula Using Hybrid Functions
by Zainab J. Kadum and Noori Y. Abdul-Hassan
Symmetry 2023, 15(3), 631; https://doi.org/10.3390/sym15030631 - 2 Mar 2023
Cited by 6 | Viewed by 3388
Abstract
In this study, we construct new numerical methods for solving the initial value problem (IVP) in ordinary differential equations based on a symmetrical quadrature integration formula using hybrid functions. The proposed methods are designed to provide an efficient and accurate solution to IVP [...] Read more.
In this study, we construct new numerical methods for solving the initial value problem (IVP) in ordinary differential equations based on a symmetrical quadrature integration formula using hybrid functions. The proposed methods are designed to provide an efficient and accurate solution to IVP and are more suitable for problems with non-smooth solutions. The key idea behind the proposed methods is to combine the advantages of traditional numerical methods, such as Runge–Kutta and Taylor’s series methods, with the strengths of modern hybrid functions. Furthermore, we discuss the accuracy and stability analysis of these methods. The resulting methods can handle a wide range of problems, including those with singularities, discontinuities, and other non-smooth features. Finally, to demonstrate the validity of the proposed methods, we provide several numerical examples to illustrate the efficiency and accuracy of these methods. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
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10 pages, 890 KiB  
Article
A Robust and Non-Fragile Observer Design for Nonlinear Fractional-Order Systems
by Omar Kahouli, Omar Naifar, Abdellatif Ben Makhlouf, Yassine Bouteraa, Ali Aloui and Ali Rebhi
Symmetry 2022, 14(9), 1795; https://doi.org/10.3390/sym14091795 - 29 Aug 2022
Cited by 2 | Viewed by 1409
Abstract
The challenge of developing observers for classical integer-order systems that are both resilient and non-fragile has received a lot of attention in the literature. However, only a few articles have addressed the topic of developing observers for Fractional-Order (FO) systems that are both [...] Read more.
The challenge of developing observers for classical integer-order systems that are both resilient and non-fragile has received a lot of attention in the literature. However, only a few articles have addressed the topic of developing observers for Fractional-Order (FO) systems that are both H-infinity H∞ and non-fragile. The current work handles the Caputo fractional-order systems as the first work, to our knowledge, which treats such problems. The authors provide a novel result for building non-fragile and robust observers for nonlinear Caputo fractional-order systems. For this, the H∞ performance method is utilized. Simulations for a numerical example confirm the efficacy of the suggested technique. The primary advantage of the current work is that it is the first to address the Caputo fractional-order system problem. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
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15 pages, 295 KiB  
Article
Generalized Inequalities of Hilbert-Type on Time Scales Nabla Calculus
by Mohammed Zakarya, Ghada AlNemer, Ahmed I. Saied, Roqia Butush, Omar Bazighifan and Haytham M. Rezk
Symmetry 2022, 14(8), 1512; https://doi.org/10.3390/sym14081512 - 24 Jul 2022
Cited by 5 | Viewed by 1442
Abstract
In this paper, we prove some new generalized inequalities of Hilbert-type on time scales nabla calculus by applying Hölder’s inequality, Young’s inequality, and Jensen’s inequality. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
24 pages, 321 KiB  
Article
Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales
by Haytham M. Rezk, Ghada AlNemer, Ahmed I. Saied, Omar Bazighifan and Mohammed Zakarya
Symmetry 2022, 14(4), 750; https://doi.org/10.3390/sym14040750 - 6 Apr 2022
Cited by 7 | Viewed by 1391
Abstract
This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power β,β>1. The main [...] Read more.
This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power β,β>1. The main results are proved by using Specht’s ratio, chain rule and Jensen’s inequality. Our results (when T=N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
13 pages, 495 KiB  
Article
Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model
by Ghazi Abed Meften, Ali Hasan Ali, Khalil S. Al-Ghafri, Jan Awrejcewicz and Omar Bazighifan
Symmetry 2022, 14(3), 565; https://doi.org/10.3390/sym14030565 - 13 Mar 2022
Cited by 21 | Viewed by 2872
Abstract
The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and [...] Read more.
The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F=0 and the case of the Taylor-Darcy number τ=0. For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
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The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

 
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