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
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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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