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Axioms
Special Issues
Differential and Dynamic Equations on Time Scales and Their Applications
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Differential and Dynamic Equations on Time Scales and Their Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 June 2024) | Viewed by 6237

Special Issue Editors

Prof. Dr. Svetlin G. Georgiev

E-Mail Website
Guest Editor
1. Faculty of Mathematics and Informatics, Sorbonne University, Paris, France
2. Department of Differential Equations, Sofia University, Sofia, Bulgaria
Interests: differential geometry; dynamic geometry; time scale calculus; dynamic equations on time scales; integral equations; ordinary differential equations; partial differential equations; stochastic differential equations; clifford algebras; clifford analysis; quaternion analysis; iso-mathematics
Special Issues, Collections and Topics in MDPI journals
Dr. Khaled Zennir

E-Mail Website
Guest Editor
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
Interests: stochastic partial differential equations; stochastic ordinary differential equations; time scale calculus; harmonic analysis; ordinary and partial differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue on ‘Differential and Dynamic Equations on Time Scales and their Applications’ publishes papers dealing with new research on time scale calculations, including: ordinary and partial differential equations; time scale calculus; developments in full, partial, functional, fractional, fuzzy, and impulsive dynamic equations; integral equations and inequalities; fractional and fuzzy dynamic calculus; fractional dynamic inequalities; optimal control problems; theories of probability; numerical analysis; numerical methods to applying dynamic equations. The journal also encourages papers related to the mathematical modeling and applications of ordinary and partial differential equations and time scale calculus in biology, chemistry, physics, medicine, and computer sciences. The journal accepts high-quality papers containing original research results and survey articles.

Prof. Dr. Svetlin G. Georgiev
Dr. Khaled Zennir
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. Axioms 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

  • ordinary differential equations
  • partial differential equations
  • dynamic calculus on time scales
  • dynamic equations on time scales
  • differential inclusions
  • numerical analysis on time scales

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Published Papers (4 papers)

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Research

16 pages, 295 KB  
Article
Unified Generalizations of Hardy-Type Inequalities Through the Nabla Framework on Time Scales
by Haytham M. Rezk, Oluwafemi Samson Balogun and Mahmoud E. Bakr
Axioms 2024, 13(10), 723; https://doi.org/10.3390/axioms13100723 - 18 Oct 2024
Cited by 2 | Viewed by 885
Abstract
This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative functions. We extend these inequalities within a cohesive framework that integrates elements [...] Read more.
This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative functions. We extend these inequalities within a cohesive framework that integrates elements of both continuous and discrete calculus. Furthermore, our study revisits specific integral inequalities from the existing literature, showcasing the wide-ranging relevance of our results. Full article
(This article belongs to the Special Issue Differential and Dynamic Equations on Time Scales and Their Applications)
17 pages, 302 KB  
Article
Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces
by Safia Meftah, Elhabib Hadjadj, Mohamad Biomy and Fares Yazid
Axioms 2023, 12(11), 1063; https://doi.org/10.3390/axioms12111063 - 20 Nov 2023
Cited by 2 | Viewed by 1697
Abstract
In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some [...] Read more.
In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some notions and properties on set-valued maps and give some examples to explain our main results. We explore and use in this paper the fundamental properties of set-valued maps, which are needed for the study of differential inclusions. It began only in the mid-1900s, when mathematicians realized that their uses go far beyond a mere generalization of single-valued maps. Full article
(This article belongs to the Special Issue Differential and Dynamic Equations on Time Scales and Their Applications)
19 pages, 327 KB  
Article
Novel Hardy-Type Inequalities with Submultiplicative Functions on Time Scales Using Delta Calculus
by Haytham M. Rezk, Ahmed I. Saied, Maha Ali, Belal A. Glalah and Mohammed Zakarya
Axioms 2023, 12(8), 791; https://doi.org/10.3390/axioms12080791 - 16 Aug 2023
Cited by 2 | Viewed by 1456
Abstract
In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales delta calculus. A time scale, denoted by T, is any [...] Read more.
In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales delta calculus. A time scale, denoted by T, is any closed nonempty subset of R. In time scale calculus, results are unified and extended. As particular cases of our findings (when T=R), we have the continuous analogues of inequalities established in some the literature. Furthermore, we can find other inequalities in different time scales, such as T=N, which, to the best of the authors’ knowledge, is a largely novel conclusion. Full article
(This article belongs to the Special Issue Differential and Dynamic Equations on Time Scales and Their Applications)
12 pages, 759 KB  
Article
Classical Solutions for the Generalized Korteweg-de Vries Equation
by Svetlin Georgiev, Aissa Boukarou, Zayd Hajjej and Khaled Zennir
Axioms 2023, 12(8), 777; https://doi.org/10.3390/axioms12080777 - 10 Aug 2023
Viewed by 1351
Abstract
The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. In our system, f or p=2 and p=3 (Korteweg-de Vries equations (KdV)) and (modified Korteweg-de Vries (mKdV) respectively), these equations [...] Read more.
The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. In our system, f or p=2 and p=3 (Korteweg-de Vries equations (KdV)) and (modified Korteweg-de Vries (mKdV) respectively), these equations have many applications in Physics. (gKdV) is a Hamiltonian system. In this article we investigate the generalized Korteweg-de Vries (gKdV) equation. A new topological approach is applied to prove the existence of at least one classical solution. The arguments are based upon recent theoretical results. Full article
(This article belongs to the Special Issue Differential and Dynamic Equations on Time Scales and Their Applications)
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