Research Article
Exact Travelling Wave Solutions for the Space-time Fractional Benjamin-Ono Equation with Three Types of Fractional Operators
Yinlin Ye,
Hongtao Fan
,
Yajing Li*
Issue:
Volume 14, Issue 5, October 2025
Pages:
253-263
Received:
29 August 2025
Accepted:
8 September 2025
Published:
25 September 2025
Abstract: The space-time fractional Benjamin-Ono equation (STFBOE) is of fundamental importance in ocean science, particularly for modeling wave propagation in deep water. This study investigates the STFBOE employing three distinct fractional operators: the conformable derivative, the beta derivative, and the M-truncated derivative. By applying a fractional traveling wave transformation, the original nonlinear fractional partial differential equation is reduced to an ordinary differential equation. We then utilize three analytical techniques-the fractional functional variable method, the modified Kudryashov method, and the improved F-expansion method to derive novel exact traveling wave solutions. To the best of our knowledge, the exact solutions for the fractional Benjamin-Ono equation in the form considered here have been scarcely studied. A key contribution of this work is the introduction and tailored application of these methods to systematically construct solutions under each fractional derivative definition. Accordingly, we establish specific traveling wave variables corresponding to the conformable, beta, and M-truncated derivatives. A significant advantage of the proposed framework is its flexibility and effectiveness, enabling a straightforward derivation of solutions for both time-fractional and space-fractional versions of the Benjamin-Ono equation. Finally, we present a comparative graphical analysis of the obtained solutions using two- and three-dimensional plots, illustrating the spatio-temporal dynamics under selected parameter values. All the derived solutions are entirely new and extend the current understanding of nonlinear wave phenomena described by the STFBOE.
Abstract: The space-time fractional Benjamin-Ono equation (STFBOE) is of fundamental importance in ocean science, particularly for modeling wave propagation in deep water. This study investigates the STFBOE employing three distinct fractional operators: the conformable derivative, the beta derivative, and the M-truncated derivative. By applying a fractional ...
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Research Article
On the Classification of Certain Unitary Division Algebras
Issue:
Volume 14, Issue 5, October 2025
Pages:
264-271
Received:
15 September 2025
Accepted:
28 September 2025
Published:
22 October 2025
DOI:
10.11648/j.acm.20251405.12
Downloads:
Views:
Abstract: Nonassociative division algebras play a significant role in Physics and Communications. The finite nonassociative division algebras have a vast range of applications on coding theory, combinatorics and graph theory. This paper deals with a class of finite structures known as division algebras. For a long time division algebras have been studied from a geometric point of view, since they coordinatize certain types of projective planes as an important part of finite geometric incidence. But recent results relating division algebras and coding theory (and also the study of Generalized Galois Rings) have stimulated the study of these rings from a strictly algebraic point of view. This paper follows the second path. Let A be a unital division algebra of order of q4, q is an odd prime power greater than 3. We assume that A admits an elementary abelian automorphism group E acting freely on A, i.e A≌𝔽q[E]. The purpose of this paper is to classify this class of division algebras. In addition, we compute a bound for q and deduce relations among certain structure constants for the quartics associated with A. These relations determine A completely. To achieve these objectives an algebraic geometric approach which is mainly based on the prominent results namely Hasse-Weil theorem and Chevalley-Wraring theorem and the work of Menichetti on n-dimensional algebras over fields of cyclic extensions of degree n.
Abstract: Nonassociative division algebras play a significant role in Physics and Communications. The finite nonassociative division algebras have a vast range of applications on coding theory, combinatorics and graph theory. This paper deals with a class of finite structures known as division algebras. For a long time division algebras have been studied fro...
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Research Article
Epidemic Change Point Detection Using Nash Equilibrium
Reza Habibi*
Issue:
Volume 14, Issue 5, October 2025
Pages:
272-276
Received:
20 September 2025
Accepted:
4 October 2025
Published:
27 October 2025
DOI:
10.11648/j.acm.20251405.13
Downloads:
Views:
Abstract: The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to another. This paper explores the concept of epidemic change points through the lens of Nash equilibrium. We propose a mathematical model that incorporates the dynamics of epidemic the change point's model into game theory. Game Theory refers to a language used to model choices made by purposive agents, where the outcomes of each player are influenced by the actions of other agents. Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that players should take to secure the best outcomes. This article is worth reading because it demonstrates the use of game theory in estimating change points. It studies interactive decision-making, where the outcome for each participant or player depends on the actions of all. And it is interesting that the Nash equilibrium points of the two actors and the researcher are for optimizing their utility functions (minimizing loss functions). We demonstrate the applicability of our approach through simulations of hypothetical epidemics, revealing how game-theoretic strategies can enhance decision-making processes in real-time.
Abstract: The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to ...
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