ORIGINAL RESEARCH article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1611846
This article is part of the Research TopicInnovative Applications of Applied Mathematics in Solving Real-World ChallengesView all 3 articles
Treatment of a generalized scalar differential equation: Analysis and explicit solution
Provisionally accepted
- 1Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
- 2University of Tabuk, Tabuk, Saudi Arabia
- 3University of Bisha, BISHA, Saudi Arabia
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Obtaining a solution of a given SDE is essential in neuroscience, especially, in modeling transmission of nerve impulses between neurons through myelin substance.This paper analyzes a particular scalar differential equation (SDE). The current scalar model involves two categories of differential equations-advanced and delayed-based on the domain of the independent variable. The results are consistent with existing literature as the advance/delay parameter approaches unity. Theoretical and graphical analyses of the solution's properties are presented. To the best of our knowledge, this is the first study to analyze this form of SDE.
Keywords: Scalar differential equation, Ordinary differential equation, Delayed differential equation, Advanced differential equation. MSC: 34K07, Series
Received: 14 Apr 2025; Accepted: 04 Aug 2025.
Copyright: © 2025 Seddek, El-Zahar, Ebaid and Al Qarni. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Abdelhalim Ebaid, University of Tabuk, Tabuk, Saudi Arabia
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