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Axioms
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Differential Equations: Theories, Methods and Modern Applications
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Differential Equations: Theories, Methods and Modern Applications

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

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 9431

Special Issue Editors

Prof. Dr. Ali Shokri

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, Maragheh 55181-83111, Iran
Interests: numerical analysis; scientific computing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Samad Noeiaghdam

E-Mail Website
Guest Editor
1. Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
2. Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia
Interests: numerical analysis; solving integral equations; solving ODEs and PDEs; solving ill-posed problems; fuzzy mathematics; stochastic arithmetic; CADNA library; CESTAC method; solving biomathematical models; iterative methods; numerical methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shyam Sundar Santra

E-Mail Website1 Website2
Co-Guest Editor
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
Interests: oscillation theory of differential/difference equations; oscillation theory of impulsive differential/difference equations; hyers-ulam stability; fractional differential equations; mathematical model

Special Issue Information

Dear Colleagues,

We invite you to submit your research papers in the field of differential equations to this Special Issue, entitled “Differential Equations: Theories, Methods and Modern Applications”, of the journal Axioms. We seek studies on new and innovative approaches for solving linear and nonlinear differential equations. We also aim to cover high-dimensional problems and system of equations. We welcome submissions presenting new theoretical results, structural investigations, new models, and algorithmic approaches with new applications of mathematical and engineering problems.

Prof. Dr. Ali Shokri
Prof. Dr. Samad Noeiaghdam
Prof. Dr. Shyam Sundar Santra
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
  • System of equations
  • Fractional problems
  • Linear and nonlinear problems
  • Fuzzy problems
  • Numerical methods
  • Analytical methods
  • Semi-analytical methods
  • Convergence analysis
  • Error analysis
  • Mathematical models
  • High dimensional problems
  • Integral equations

Published Papers (4 papers)

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Research

12 pages, 406 KiB  
Article
Positive Numerical Approximation of Integro-Differential Epidemic Model
by Eleonora Messina, Mario Pezzella and Antonia Vecchio
Axioms 2022, 11(2), 69; https://doi.org/10.3390/axioms11020069 - 09 Feb 2022
Cited by 6 | Viewed by 2323
Abstract
In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive [...] Read more.
In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive conditions on the step-length of integration h, some of the essential properties of the continuous system. In particular, the numerical solution is positive and bounded and, in cases of interest in applications, it is monotone. We prove an order of convergence theorem and show by numerical experiments that the discrete final size tends to its continuous equivalent as h tends to zero. Full article
(This article belongs to the Special Issue Differential Equations: Theories, Methods and Modern Applications)
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11 pages, 278 KiB  
Article
Neutral Differential Equations of Fourth-Order: New Asymptotic Properties of Solutions
by Ali Muhib, Osama Moaaz, Clemente Cesarano, Sameh Askar and Elmetwally M. Elabbasy
Axioms 2022, 11(2), 52; https://doi.org/10.3390/axioms11020052 - 28 Jan 2022
Cited by 8 | Viewed by 1650
Abstract
In this work, we will derive new asymptotic properties of the positive solutions of the fourth-order neutral differential equation with the non-canonical factor. We follow an improved approach that enables us to create oscillation criteria of an iterative nature that can be applied [...] Read more.
In this work, we will derive new asymptotic properties of the positive solutions of the fourth-order neutral differential equation with the non-canonical factor. We follow an improved approach that enables us to create oscillation criteria of an iterative nature that can be applied more than once to test oscillation. In light of this, we will use these properties to obtain new criteria for the oscillation of the solutions of the studied equation. An example is given to show the applicability of the main results. Full article
(This article belongs to the Special Issue Differential Equations: Theories, Methods and Modern Applications)
16 pages, 490 KiB  
Article
A Probabilistic Approach for Solutions of Deterministic PDE’s as Well as Their Finite Element Approximations
by Joël Chaskalovic
Axioms 2021, 10(4), 349; https://doi.org/10.3390/axioms10040349 - 20 Dec 2021
Cited by 3 | Viewed by 1919
Abstract
A probabilistic approach is developed for the exact solution u to a deterministic partial differential equation as well as for its associated approximation uh(k) performed by Pk Lagrange finite element. Two limitations motivated our approach: On the one [...] Read more.
A probabilistic approach is developed for the exact solution u to a deterministic partial differential equation as well as for its associated approximation uh(k) performed by Pk Lagrange finite element. Two limitations motivated our approach: On the one hand, the inability to determine the exact solution u relative to a given partial differential equation (which initially motivates one to approximating it) and, on the other hand, the existence of uncertainties associated with the numerical approximation uh(k). We, thus, fill this knowledge gap by considering the exact solution u together with its corresponding approximation uh(k) as random variables. By a method of consequence, any function where u and uh(k) are involved are modeled as random variables as well. In this paper, we focus our analysis on a variational formulation defined on Wm,p Sobolev spaces and the corresponding a priori estimates of the exact solution u and its approximation uh(k) in order to consider their respective Wm,p-norm as a random variable, as well as the Wm,p approximation error with regards to Pk finite elements. This will enable us to derive a new probability distribution to evaluate the relative accuracy between two Lagrange finite elements Pk1 and Pk2,(k1<k2). Full article
(This article belongs to the Special Issue Differential Equations: Theories, Methods and Modern Applications)
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13 pages, 278 KiB  
Article
On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators
by Erhan Set, Ahmet Ocak Akdemir, Ali Karaoǧlan, Thabet Abdeljawad and Wasfi Shatanawi
Axioms 2021, 10(3), 223; https://doi.org/10.3390/axioms10030223 - 12 Sep 2021
Cited by 3 | Viewed by 1592
Abstract
Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation [...] Read more.
Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals. Full article
(This article belongs to the Special Issue Differential Equations: Theories, Methods and Modern Applications)
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