Treatment of a generalized scalar differential equation: analysis and explicit solution

Laila F. Seddek; Essam R. El-Zahar; Abdelhalim Ebaid; A. A. Al Qarni

doi:10.3389/fphy.2025.1611846

Frontiers in Physics (Sep 2025)

Treatment of a generalized scalar differential equation: analysis and explicit solution

Laila F. Seddek,
Essam R. El-Zahar,
Abdelhalim Ebaid,
A. A. Al Qarni

Affiliations

Laila F. Seddek: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia
Essam R. El-Zahar: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia
Abdelhalim Ebaid: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
A. A. Al Qarni: Department of Mathematics, College of Science, University of Bisha, Bisha, Saudi Arabia

DOI: https://doi.org/10.3389/fphy.2025.1611846
Journal volume & issue: Vol. 13

Abstract

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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.

Published in Frontiers in Physics

ISSN: 2296-424X (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Science: Physics
Website: https://www.frontiersin.org/journals/physics

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