Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.6
Journals
Axioms
Special Issues
Difference, Functional, and Related Equations, 2nd Edition
share announcement

Difference, Functional, and Related Equations, 2nd Edition

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

Deadline for manuscript submissions: closed (30 April 2026) | Viewed by 2940

Special Issue Editors

Dr. Ravi Shankar

E-Mail Website
Guest Editor
Department of Mathematics, Princeton University, Princeton, NJ, USA
Interests: fully nonlinear elliptic PDEs without uniform ellipticity (sigma-k and special Lagrangian equations); inverse problems of the lens rigidity and Calderón type; symmetries and conservation laws of fluid equations and general PDEs; applied mathematics, including numerical simulations of tsunami waves, singular perturbation theory of thin film PDEs, and non-local operators with integrable kernels
Special Issues, Collections and Topics in MDPI journals
Dr. Qun Liu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Interests: stochastic differential equations and their applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to collect and showcase original and interesting results related to difference, functional, stochastic, and related equations with non-local characters. Articles that deepen our understanding of non-local equations and their applicability are sought. The scope includes but is not limited to: 1. difference equations and related areas such as fractional difference equations, recursion relations, numerical and computational methods for equations, generating functions, and series; 2. functional equations and related topics, including delay equations, functional differential equations, delay differential equations, fractional functional, delay, and other equations; 3. stochastic equations and related topics; 4. applications of non-local equations to natural and social sciences; and 5. other new aspects and applications of non-local equations.

Dr. Ravi Shankar
Dr. Qun Liu
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 250 words) can be sent to the Editorial Office for assessment.

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

  • difference equations
  • functional equations
  • delay differential equations
  • fractional difference and other equations
  • numerical methods for equations
  • stochastic equation
  • stochastic analysis
  • applications to natural and social sciences

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Review

23 pages, 519 KB  
Article
On the Periodicity and Solvability of Multi-Shift Three-Dimensional Difference Systems
by Yasser Almoteri and Ahmed Ghezal
Axioms 2026, 15(6), 400; https://doi.org/10.3390/axioms15060400 - 26 May 2026
Viewed by 74
Abstract
This paper investigates the closed-form solvability and dynamical behavior of a class of nonlinear triangular difference systems with overlapping indices, emphasizing the role of coefficient symmetry and asymmetry in determining the qualitative behavior of the system. A unified analytical framework is developed by [...] Read more.
This paper investigates the closed-form solvability and dynamical behavior of a class of nonlinear triangular difference systems with overlapping indices, emphasizing the role of coefficient symmetry and asymmetry in determining the qualitative behavior of the system. A unified analytical framework is developed by transforming the original nonlinear system into equivalent linear or multiplicative difference equations, thereby enabling the derivation of explicit general solutions for various parameter configurations. The results show that the structure of the coefficients plays a fundamental role in determining stability, periodicity, and long-term dynamics. In particular, symmetric configurations tend to produce regular and more structured periodic behavior, whereas asymmetric configurations lead to more irregular oscillatory patterns and increased sensitivity to initial conditions. These theoretical findings are supported by numerical simulations and graphical illustrations, which demonstrate how variations in coefficient values and signs influence the evolution of the system. Finally, an application to discrete survival dynamics is presented, illustrating the capability of the proposed model to describe interacting survival processes under both symmetric and asymmetric parameter regimes, thereby highlighting its potential relevance in the study of applied discrete dynamical systems. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
►▼ Show Figures

Figure 1

13 pages, 1002 KB  
Article
Lie Symmetry and Various Exact Solutions for (3+1)-Dimensional B-Type Kadomtsev–Petviashvili Equation
by Ahmed A. Gaber, Dalal Alhwikem and Abdul-Majid Wazwaz
Axioms 2026, 15(2), 156; https://doi.org/10.3390/axioms15020156 - 22 Feb 2026
Cited by 1 | Viewed by 396
Abstract
The (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) problem was examined in this paper using the developed Exp-function method (DEFM) and Lie symmetry analysis. The objective of this research is studying the BKP equation to get novel exact solutions. Symmetry analysis has been used to determine [...] Read more.
The (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) problem was examined in this paper using the developed Exp-function method (DEFM) and Lie symmetry analysis. The objective of this research is studying the BKP equation to get novel exact solutions. Symmetry analysis has been used to determine similarity variables and vector fields. The governing equation was reduced to five variant ordinary differential equations (ODEs). The DEFM was employed for four of them to obtain several novel exact solutions that contain arbitrary constants. The most appropriate choice of values for these optional constants contributed to the emergence of solutions, such as double waves, multisolitons, kink waves, anti-kink waves, and solitary waves. The obtained exact solutions are presented in a 3D graph. The behavior of the solutions can be utilized to explore the application of the governing equation in fluid dynamics, plasma physics, nonlinear optics, and ocean physics. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
►▼ Show Figures

Figure 1

18 pages, 288 KB  
Article
Functional Differential Equations with Non-Canonical Operator: Oscillatory Features of Solutions
by Asma Al-Jaser, Faizah Alharbi, Dimplekumar Chalishajar and Belgees Qaraad
Axioms 2025, 14(8), 588; https://doi.org/10.3390/axioms14080588 - 29 Jul 2025
Cited by 4 | Viewed by 763
Abstract
This study focuses on investigating the asymptotic and oscillatory behavior of a new class of fourth-order nonlinear neutral differential equations. This research aims to achieve a qualitative advancement in the analysis and understanding of the relationships between the corresponding function and its derivatives. [...] Read more.
This study focuses on investigating the asymptotic and oscillatory behavior of a new class of fourth-order nonlinear neutral differential equations. This research aims to achieve a qualitative advancement in the analysis and understanding of the relationships between the corresponding function and its derivatives. By utilizing various techniques, innovative criteria have been developed to ensure the oscillation of all solutions of the studied equations without resorting to additional constraints. Effective analytical tools are provided, contributing to a deeper theoretical understanding and expanding their application scope. The paper concludes by presenting examples that illustrate the practical impact of the results, highlighting the theoretical value of the research in the field of functional differential equations. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
15 pages, 4808 KB  
Article
Unveiling the Transformative Power: Exploring the Nonlocal Potential Approach in the (3 + 1)-Dimensional Yu–Toda–Sasa–Fukuyama Equation
by Enas Y. Abu El Seoud, Ahmed S. Rashed and Samah M. Mabrouk
Axioms 2025, 14(4), 298; https://doi.org/10.3390/axioms14040298 - 15 Apr 2025
Viewed by 955
Abstract
This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, [...] Read more.
This paper focuses on the investigation of the Yu–Toda–Sasa–Fukuyama (YTSF) equation in its three-dimensional form. Based on the well-known Euler operator, a set of seven non-singular local multipliers is explored. Using these seven non-singular multipliers, the corresponding local conservation laws are derived. Additionally, an auxiliary potential-related system of partial differential equations (PDEs) is constructed. This study delves into nonlocal systems, which reveal numerous intriguing exact solutions of the YTSF equation. The nonlinear systems exhibit stable structures such as kink solitons, representing transitions, and breather or multi-solitons, modeling localized energy packets and complex interactions. These are employed in materials science, optics, communications, and plasma. Additionally, patterns such as parabolic backgrounds with ripples inform designs involving structured or varying media such as waveguides. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
►▼ Show Figures

Figure 1

Review

Jump to: Research

40 pages, 523 KB  
Review
Explicit Solutions of Linear Discrete Delay Systems: A Comprehensive Survey of Delayed Matrix Functions and Their Applications
by Fatemah Mofarreh and Ahmed M. Elshenhab
Axioms 2026, 15(5), 341; https://doi.org/10.3390/axioms15050341 - 6 May 2026
Viewed by 201
Abstract
This survey provides a systematic review of delayed matrix functions and their role in deriving explicit solutions for linear discrete delay systems. Tracing the evolution from foundational single-delay first-order systems to sophisticated multi-delay configurations, we cover delayed matrix exponentials, sines, and cosines for [...] Read more.
This survey provides a systematic review of delayed matrix functions and their role in deriving explicit solutions for linear discrete delay systems. Tracing the evolution from foundational single-delay first-order systems to sophisticated multi-delay configurations, we cover delayed matrix exponentials, sines, and cosines for both commutative and non-commutative coefficient matrices, as well as generalizations for two-sided delay terms. We synthesize closed-form solution representations for a wide spectrum of initial value problems and highlight applications across stability analysis, controllability, iterative learning control, and finite-time stability. The paper concludes with a critical discussion identifying open problems-including extensions to higher-order differences, Volterra-type systems, and non-commutative multi-delay scenarios-serving as a unified reference connecting algebraic construction to analytical utility in linear discrete dynamical systems with memory. The review is reported in accordance with the PRISMA 2020 guidelines; the completed checklist and flow diagram are provided. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations, 2nd Edition)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop