@article{Castro2025, 
author = {Luís P. Castro and Edixon M. Rojas},
title = {On the existence and stability of bounded solutions for a class of three-point boundary value problems of fractional type},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20909-20931},
keywords = {boundary value problem, fractional differential equation, stability, nonlocal boundary condition, Lp-Carathéodory condition, weakly singular kernel, Gronwall-type inequality, Riemann-Liouville fractional derivative},
url = {https://www.sciopen.com/article/10.3934/math.2025934},
doi = {10.3934/math.2025934},
abstract = {This article investigates the existence and stability of solutions for a class of three-point boundary value problems involving Riemann-Liouville fractional derivatives of order less than one. We considered nonlinear fractional differential equations subject to nonlocal boundary conditions that include a singular condition at the origin and a global fractional condition at interior points. Our approach generalizes previous work, allowing for singular behavior near zero, and employs the Leray-Schauder fixed point theorem to establish the existence of bounded solutions without requiring contractive conditions on the nonlinear term. Instead, we imposed a local integrability condition known as the        L    p  -Carathéodory condition. Furthermore, we studied the Ulam-Hyers-Rassias stability of approximate solutions by means of a Gronwall-type inequality adapted to weakly singular kernels. Two concrete examples were also included to illustrate the theory.}
}