Exploring existence, uniqueness, and stability in nonlinear fractional boundary value problems with three-point boundary conditions

Abstract This study investigates the analysis of the existence, uniqueness, and stability of solutions for a $\Psi$-Caputo three-point nonlinear fractional boundary value problem using the Banach contraction principle and Sadovskii's fixed point theorem. We demonstrate the practical implications of our analytical advancements for each situation, illustrating how the components of the fractional boundary value problem emerge in real-life occurrences. Our work significantly enhances the field of applied mathematics by offering analytical solutions and valuable insights.