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Axioms
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Mathematical Methods in the Applied Sciences, 2nd Edition
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Mathematical Methods in the Applied Sciences, 2nd Edition

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 2514

Special Issue Editors

Dr. Nuno Bastos

E-Mail Website
Guest Editor
Department of Mathematics, ESTGV Polytechnic Institute of Viseu, 3504-510 Viseu, Portugal
Interests: calculus of variations; time scales; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Dr. Touria Karite

E-Mail Website
Guest Editor
Department of Applied Mathematics Engineering Department, National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco
Interests: control theory; controllability; nonlinear dynamics; optimal control; distributed systems; optimization methods; systems theory; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Dr. Ahmed Aberqi

E-Mail Website
Guest Editor
ENSA, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Interests: functional analysis; operator theory; numerical analysis; nonlinear partial differential equations; nonlinear analysis; optimal control theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue, entitled "Mathematical Methods in the Applied Sciences". Applied sciences encompass a wide array of fields, including engineering, business, medicine, neuroscience, Earth science, quantum computing, and epidemiology. Unlike basic science, which aims to develop theories and laws to explain and predict natural phenomena, applied sciences use mathematical approaches to solve practical problems. This necessitates the search for and development of appropriate mathematical methods to accurately describe and explain real-world phenomena, often involving linear and non-linear equations, as well as ordinary and partial differential equations.

The objective of this Special Issue is to provide a platform for scientists and researchers to present their work on topics such as optimization, optimal control theory, biomathematics, population dynamics, network problems, reinforcement learning, machine learning, and deep learning. This will contribute to a deeper understanding of the world through the use of advanced mathematical methods.

Dr. Nuno Bastos
Dr. Touria Karite
Dr. Ahmed Aberqi
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

  • mathematical methods
  • analysis
  • applied mathematics
  • biomathematics
  • modeling
  • applied sciences
  • real systems
  • applied mechanics
  • quantitative models
  • simulation methodology
  • inverse problems
  • numerical methods
  • machine learning
  • deep learning
  • reinforcement learning

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Related Special Issue

Published Papers (2 papers)

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Research

15 pages, 6457 KiB  
Article
Rationality Levels in a Heterogeneous Dynamic Price Game
by Min Guo and Qiqing Song
Axioms 2025, 14(3), 194; https://doi.org/10.3390/axioms14030194 - 5 Mar 2025
Viewed by 345
Abstract
The Bertrand game is one of the basic game models in modern microeconomics. In some behavior experiments with game theory, it was shown that agents have different bounded rationality levels. In order to check the effect of bounded rationality levels on the stability [...] Read more.
The Bertrand game is one of the basic game models in modern microeconomics. In some behavior experiments with game theory, it was shown that agents have different bounded rationality levels. In order to check the effect of bounded rationality levels on the stability of the equilibrium points in Bertrand games, this study establishes a new dynamic price game with a parameter to show the rationality levels. An exact geometrical characterization of the stable region of the dynamic system is firstly proposed, from which the critical points of the bifurcation of the system can be deduced. It is shown that allowing various bounded rationalities is conducive to enlarging the stable region of the equilibrium point of the price system. With increasing rationality level, the stable region expands. Numerical examples are provided to show the main results. Full article
(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences, 2nd Edition)
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23 pages, 3190 KiB  
Article
Numerical Solution of Mathematical Model of Heat Conduction in Multi-Layered Nanoscale Solids
by Aníbal Coronel, Ian Hess, Fernando Huancas and José Chiroque
Axioms 2025, 14(2), 105; https://doi.org/10.3390/axioms14020105 - 30 Jan 2025
Viewed by 506
Abstract
In this article, we are interested in studying and analyzing the heat conduction phenomenon in a multi-layered solid. We consider the physical assumptions that the dual-phase-lag model governs the heat flow on each solid layer. We introduce a one-dimensional mathematical model given by [...] Read more.
In this article, we are interested in studying and analyzing the heat conduction phenomenon in a multi-layered solid. We consider the physical assumptions that the dual-phase-lag model governs the heat flow on each solid layer. We introduce a one-dimensional mathematical model given by an initial interface-boundary value problem, where the unknown is the solid temperature. More precisely, the mathematical model is described by the following four features: the model equation is given by a dual-phase-lag equation at the inside each layer, an initial condition for temperature and the temporal derivative of the temperature, heat flux boundary conditions, and the interfacial condition for the temperature and heat flux conditions between the layers. We discretize the mathematical model by a finite difference scheme. The numerical approach has similar features to the continuous model: it is considered to be the accuracy of the dual-phase-lag model on the inside each layer, the initial conditions are discretized by the average of the temperature on each discrete interval, the inside of each layer approximation is extended to the interfaces by using the behavior of the continuous interface conditions, and the inside each layer approximation on the boundary layers is extended to state the numerical boundary conditions. We prove that the finite difference scheme is unconditionally stable and unconditionally convergent. In addition, we provide some numerical examples. Full article
(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences, 2nd Edition)
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