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Axioms
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Advances in Difference Equations
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Special Issue "Advances in Difference Equations"

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

Deadline for manuscript submissions: 20 July 2023 | Viewed by 1194

Special Issue Editors

Dr. Azhar Ali Zafar

E-Mail Website
Guest Editor
Department of Mathematics, Government College University, Lahore 54770, Pakistan
Interests: dynamical systems
Dr. Nehad Ali Shah

E-Mail Website
Guest Editor
Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Interests: fluid dynamics (Newtonian and non-Newtonian fluids; heat and mass transfer; viscoelastic models with memory; fractional thermoelasticity)

Special Issue Information

Dear Colleagues,

As we are all aware, the extreme nature of difference equations’ representations of complex dynamical systems is widely recognized. The kernel of fractional order derivative operators has its own relevance as an empirical explanation of such complex phenomena, and the theory of fractional derivative operators has been successfully applied in recent years to study anomalous social and physical sciences. The difference counterpart of fractional calculus has been increasingly used to describe many occurrences that take place in the real world. Many academic fields, significantly the biological sciences, have started to place a substantial emphasis on systems of delay differential equations.

This Special Issue will accept top-notch papers with unique research findings and focuses on the theory and applications of differential and difference equations, particularly in science and engineering. Moreover, the goal of this Special Issue is to bring together mathematicians, physicists, and other scientists to a platform of differential and difference equations where they can present their beneficial research to the intellectual community.

Dr. Azhar Ali Zafar
Dr. Nehad Ali Shah
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 1600 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

  • difference equations
  • fractional difference equations
  • delay difference equations
  • weak solutions difference equations
  • numerical methods for difference equations
  • asymptotic behavior for difference equations

Published Papers (2 papers)

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Article
Study of Burgers–Huxley Equation Using Neural Network Method
by
Ying Wen
and
Temuer Chaolu
Axioms 2023, 12(5), 429; https://doi.org/10.3390/axioms12050429 - 26 Apr 2023
Viewed by 442
Abstract
The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for solving Burgers–Huxley nonlinear partial differential equations, [...] Read more.
The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for solving Burgers–Huxley nonlinear partial differential equations, considering initial or boundary value terms in the loss functions. The proposed technique yields closed analytic solutions that possess excellent generalization properties. Our approach differs from existing deep neural networks in that it employs only shallow neural networks. This choice significantly reduces the parameter cost while retaining the dynamic behavior and accuracy of the solution. A thorough comparison with its exact solution was carried out to validate the practicality and effectiveness of our proposed method, using vivid graphics and detailed analysis to present the results. Full article
(This article belongs to the Special Issue Advances in Difference Equations)
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Article
Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions
by
Jehad Alzabut
,
Said R. Grace
,
Jagan Mohan Jonnalagadda
,
Shyam Sundar Santra
and
Bahaaeldin Abdalla
Axioms 2023, 12(4), 325; https://doi.org/10.3390/axioms12040325 - 27 Mar 2023
Viewed by 412
Abstract
This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main [...] Read more.
This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions’ non-oscillatory behavior. Full article
(This article belongs to the Special Issue Advances in Difference Equations)
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