@article{Cui2025, 
author = {Yujun Cui and Chunyu Liang and Yumei Zou},
title = {Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {3797-3818},
keywords = {Leray-Schauder continuity theorem, the existence and uniqueness of solutions, Schauder fixed point theorem, Banach fixed point theorem, Riemann–Liouville fractional derivatives},
url = {https://www.sciopen.com/article/10.3934/math.2025176},
doi = {10.3934/math.2025176},
abstract = {This study investigates boundary value problems for nonlinear fractional-order differential equations. The differential operator is interpreted in the Riemann-Liouville sense and is coupled with a non-linearrrrr term that involves the fractional derivative of the unknown function. Using the Schauder fixed point theorem, the Banach fixed point theorem, and the Leray-Schauder continuation theorem, we establish results regarding the existence and uniqueness of solutions within suitable function spaces. Additionally, we provide concrete examples of various boundary value problems involving fractional-order differential equations to demonstrate the applicability of the theory developed.}
}