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

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1611846

DOI=10.3389/fphy.2025.1611846

ISSN=2296-424X

ABSTRACT=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.