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: 29 August 2025 | Viewed by 189

Special Issue Editors


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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
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

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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

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Published Papers (1 paper)

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Research

15 pages, 4808 KiB  
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 107
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)
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