@article{Hammad2025, 
author = {Hasanen A. Hammad and Manal Elzain Mohamed Abdalla},
title = {Modified    ℜ-rational contractions and fixed point results with applications to boundary value problems},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20385-20411},
keywords = {fixed point technique, ℜ-rational contraction mapping, transverse oscillation bar, boundary value problem, evaluation metrics},
url = {https://www.sciopen.com/article/10.3934/math.2025911},
doi = {10.3934/math.2025911},
abstract = {This manuscript introduces modified    ℜ-rational contractions for single self-maps, leveraging    ω-distance in a relational-theoretic metric space. This novel approach establishes the existence and uniqueness of a fixed point for self-maps, specifically by applying the locally    Θ-transitivity property. We support our theoretical advancements with compelling examples and demonstrate their practical significance by solving a fourth-order boundary value problem related to transverse oscillation in a homogeneous bar and a first-order periodic boundary value problem.}
}