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Mathematics
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Advances in Mathematics: Equations, Algebra, and Discrete Mathematics
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Advances in Mathematics: Equations, Algebra, and Discrete Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 1 May 2025 | Viewed by 4279

Special Issue Editor

Dr. Arsen Palestini

E-Mail Website
Guest Editor
MEMOTEF, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
Interests: game theory; ordinary differential equations; mathematical economics; voting games
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is with great pleasure that I introduce a new and exciting project, specifically devoted to exploring the rich and dynamic fields of equations, algebra, and discrete mathematics. Algebra, as one of the foundational pillars of mathematical sciences, continues to captivate and challenge us with its deep complexities and structures. Equations, both differential and difference, are crucial in understanding dynamic systems and modeling various phenomena, while discrete mathematics opens up pathways to computational innovations and theoretical advancements.

This Special Issue aims to be as inclusive as possible. I am particularly interested in novel contributions in these areas, including but not limited to studies on number theory, algebraic topology, computational algebra, algebraic curves and surfaces, algebraic combinatorics, complex equations, and discrete mathematics.

I encourage researchers and scholars from all over the world to submit their high-quality papers to this Special Issue. I am sure that a lot of new and interesting results will be published and appreciated by the mathematical community worldwide.

Dr. Arsen Palestini
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. 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

  • primes
  • conjecture
  • analytic number theory
  • discrete mathematics
  • Diophantine equations
  • finite fields
  • approximation of constants
  • continued fractions
  • Ramanujan theories
  • algebraic equations
  • additive number theory
  • algebraic combinatorics
  • algebraic topology

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

20 pages, 311 KiB  
Article
On Ulam–Hyers–Mittag-Leffler Stability of Fractional Integral Equations Containing Multiple Variable Delays
by Osman Tunç and Cemil Tunç
Mathematics 2025, 13(4), 606; https://doi.org/10.3390/math13040606 - 12 Feb 2025
Cited by 1 | Viewed by 515
Abstract
In recent decades, many researchers have pointed out that derivatives and integrals of the non-integer order are well suited for describing various real-world materials, for example, polymers. It has also been shown that fractional-order mathematical models are more effective than integer-order mathematical models. [...] Read more.
In recent decades, many researchers have pointed out that derivatives and integrals of the non-integer order are well suited for describing various real-world materials, for example, polymers. It has also been shown that fractional-order mathematical models are more effective than integer-order mathematical models. Thereby, given these considerations, the investigation of qualitative properties, in particular, Ulam-type stabilities of fractional differential equations, fractional integral equations, etc., has now become a highly attractive subject for mathematicians, as this represents an important field of study due to their extensive applications in various branches of aerodynamics, biology, chemistry, the electrodynamics of complex media, polymer science, physics, rheology, and so on. Meanwhile, the qualitative concepts called Ulam–Hyers–Mittag-Leffler (U-H-M-L) stability and Ulam–Hyers–Mittag-Leffler–Rassias (U-H-M-L-R) stability are well-suited for describing the characteristics of fractional Ulam-type stabilities. The Banach contraction principle is a fundamental tool in nonlinear analysis, with numerous applications in operational equations, fractal theory, optimization theory, and various other fields. In this study, we consider a nonlinear fractional Volterra integral equation (FrVIE). The nonlinear terms in the FrVIE contain multiple variable delays. We prove the U-H-M-L stability and U-H-M-L-R stability of the FrVIE on a finite interval. Throughout this article, new sufficient conditions are obtained via six new results with regard to the U-H-M-L stability or the U-H-M-L-R stability of the FrVIE. The proofs depend on Banach’s fixed-point theorem, as well as the Chebyshev and Bielecki norms. In the particular case of the FrVIE, an example is delivered to illustrate U-H-M-L stability. Full article
(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)
20 pages, 356 KiB  
Article
Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces
by Nurzhan Bokayev, Victor Burenkov, Dauren Matin and Aidos Adilkhanov
Mathematics 2024, 12(22), 3533; https://doi.org/10.3390/math12223533 - 12 Nov 2024
Cited by 1 | Viewed by 1149
Abstract
In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces GMpθw(·). Our main result is the compactness of the commutators of the Riesz potential b,Iα [...] Read more.
In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces GMpθw(·). Our main result is the compactness of the commutators of the Riesz potential b,Iα in global Morrey-type spaces from GMp1θ1w1(·) to GMp2θ2w2(·). We also present new sufficient conditions for the commutator b,Iα to be bounded from GMp1θ1w1(·) to GMp2θ2w2(·). In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential b,Iα in global Morrey-type spaces GMpθw(·), and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces GMpθw(·). Full article
(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)
15 pages, 278 KiB  
Article
Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions
by Cemil Tunç and Fahir Talay Akyildiz
Mathematics 2024, 12(18), 2799; https://doi.org/10.3390/math12182799 - 10 Sep 2024
Cited by 1 | Viewed by 1293
Abstract
We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply [...] Read more.
We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply the method of progressive contractions, which belongs to T.A. Burton, to Caputo fractional-order differential equation, including multiple variable delays, which has not yet appeared in the relevant literature by this time. The significant point of the method of progressive contractions consists of a very flexible idea to discuss the uniqueness of solutions for various mathematical models. Lastly, we provide two examples to demonstrate how this paper’s primary outcome can be applied. Full article
(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)
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