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Axioms
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Axioms on Advanced Differential Equations for Mathematical Modeling
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Axioms on Advanced Differential Equations for Mathematical Modeling

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 9899

Special Issue Editor

Dr. Ioannis Dassios

E-Mail Website
Guest Editor
School of Electrical and Electronic Engineering, University College Dublin, D04 V1W8 Dublin, Ireland
Interests: differential/difference equations; dynamical systems; modeling and stability analysis of electric power systems; mathematics of networks; fractional calculus; mathematical modeling (power systems, materials science, energy, macroeconomics, social media, etc.); optimization for the analysis of large-scale data sets; fluid mechanics; discrete calculus; Bayes control; e-learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, many authors have studied problems of a number of different classes of advanced differential equations. The interest in studying advanced differential equations is also caused by the fact that they appear in models of several areas in science.

This Special Issue aims at collecting the latest results on axioms in advanced differential equations and also other areas of Applied Mathematics that are related to them, such as partial differential equations, difference equations, fractional calculus, mathematics of networks, optimization, etc.

These results are expected to be useful for mathematical modeling, and applications in electrical power systems, materials, energy, macroeconomics, etc.

This Special Issue will accept high-quality papers having original research results, and its purpose is to bring together mathematicians with physicists, engineers, as well as other scientists.

Topics covered include but are not limited to:

  • Differential/difference equations
  • Dynamical systems
  • Mathematics of networks
  • Fractional calculus
  • Modelling and stability analysis of power systems
  • Discrete calculus
  • Circuits theory
  • Signal processing
  • Materials science
  • Energy systems
  • Macroeconomics

Prof. Dr. Ioannis Dassios
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. 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

  • differential equations
  • fractional calculus
  • networks
  • axioms
  • mathematical modeling
  • advanced
  • singular

Published Papers (3 papers)

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Research

17 pages, 2825 KiB  
Article
On Λ-Fractional Viscoelastic Models
by Anastassios K. Lazopoulos and Dimitrios Karaoulanis
Axioms 2021, 10(1), 22; https://doi.org/10.3390/axioms10010022 - 20 Feb 2021
Cited by 5 | Viewed by 2128
Abstract
Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving. To put it straightforwardly, Λ-Fractional Derivative might be the only authentic non-local derivative [...] Read more.
Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving. To put it straightforwardly, Λ-Fractional Derivative might be the only authentic non-local derivative that exists. In the present article, Λ-Fractional Derivative is used to describe the phenomenon of viscoelasticity, while the whole methodology is demonstrated meticulously. The fractional viscoelastic Zener model is studied, for relaxation as well as for creep. Interesting results are extracted and compared to other methodologies showing the value of the pre-mentioned method. Full article
(This article belongs to the Special Issue Axioms on Advanced Differential Equations for Mathematical Modeling)
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16 pages, 461 KiB  
Article
Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations
by Marouane Mahrouf, Adnane Boukhouima, Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres and Noura Yousfi
Axioms 2021, 10(1), 18; https://doi.org/10.3390/axioms10010018 - 07 Feb 2021
Cited by 32 | Viewed by 4713
Abstract
The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported [...] Read more.
The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results. Full article
(This article belongs to the Special Issue Axioms on Advanced Differential Equations for Mathematical Modeling)
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11 pages, 252 KiB  
Article
On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays
by Shyam Sundar Santra, Ioannis Dassios and Tanusri Ghosh
Axioms 2020, 9(4), 134; https://doi.org/10.3390/axioms9040134 - 18 Nov 2020
Cited by 18 | Viewed by 2102
Abstract
In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear [...] Read more.
In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results. Full article
(This article belongs to the Special Issue Axioms on Advanced Differential Equations for Mathematical Modeling)
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