-
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 ...
Show More
-
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...
Show More
-
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 ...
Show More
-
Research Article
Brownian Motion and Thermophoretic Effect on Thin-Film Copper Nanofluid Flow over a Stretching Sheet
Issue:
Volume 14, Issue 5, October 2025
Pages:
277-292
Received:
30 September 2025
Accepted:
18 October 2025
Published:
31 October 2025
DOI:
10.11648/j.acm.20251405.14
Downloads:
Views:
Abstract: The rapid expansion of industrial and engineering activities has introduced new and complex heat transfer challenges. Many modern systems operate under conditions that require high thermal loads, thereby demanding effective heat management strategies. To address this, advancements in nanotechnology have been employed to improve the thermal performance of conventional fluids. In this study, nanoparticles were uniformly dispersed within a base fluid to enhance its thermal conductivity, leading to a significant improvement in convective heat transfer rates. The mathematical formulation of the problem involved the continuity, momentum, energy, and concentration equations, which were expressed as partial differential equations (PDEs). Through the application of similarity transformations, these equations were reduced to a system of nonlinear ordinary differential equations (ODEs). The transformed equations were then solved numerically using the collocation method (BVP4C) implemented in MATLAB, a robust solver known for its stability and accuracy in boundary value problems. The obtained results demonstrated that the presence of nanoparticles considerably improves the heat transfer characteristics of the fluid by enhancing both the temperature and velocity distributions. These findings provide valuable insights for the development of advanced nanofluids with optimized thermal properties. Such fluids hold great potential for use as efficient coolants in a wide range of applications, including electronic device cooling, automotive thermal systems, air conditioning units, and power generation equipment, where enhanced thermal management is essential for operational reliability and energy efficiency.
Abstract: The rapid expansion of industrial and engineering activities has introduced new and complex heat transfer challenges. Many modern systems operate under conditions that require high thermal loads, thereby demanding effective heat management strategies. To address this, advancements in nanotechnology have been employed to improve the thermal performa...
Show More
-
Research Article
Mathematical Modelling of Gambling Addiction Dynamics in Society
Hillary Kiprop Kosgei*,
Phylis Jerotich Kibet
Issue:
Volume 14, Issue 5, October 2025
Pages:
293-300
Received:
8 October 2025
Accepted:
18 October 2025
Published:
31 October 2025
DOI:
10.11648/j.acm.20251405.15
Downloads:
Views:
Abstract: Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to understand and manage a gambling problem in society. The basic properties of the model were established to show that the model is mathematically and biologically feasible. The basic reproduction number, ℜ0 was obtained using the next generation matrix method. The conditions for the existence of gambling free equilibrium and gambling endemic equilibrium were established, that is, both equilibria states were found to be locally and globally asymptotically stable whenever ℜ0 < 1 and unstable when ℜ0 > 1. Numerical simulation results shows that management of gambling problem depends on the control efforts invested, for instance, higher control efforts increase the chances of overcoming the challenge. The model results further reveal that the rate of contact between susceptible individuals and gamblers (casual and heavy) influences the development of gambling habits in the community. The study findings also show that serious early gambling interventions play a predominant role in mitigating this harmful behavior in society.
Abstract: Gambling addiction is a silent monster that pose a serious public health threat globally. For instance, compulsive gambling has led to family breakdowns, legal troubles, financial ruins, significant health issues, strained relationships, or even loss of lives. In this study, we formulate and analyze a gambling addiction mathematical model to unders...
Show More
