This study explores the analytical and qualitative properties of the integral solution of \(\psi \) -Hilfer fractional integro-differential equation ( \(\psi \) -HFIDE) of order \(1 < \mathfrak {u} \le 2\) , which involves nonlocal integral boundary conditions, using the concept of fixed point theory. By imposing Lipschitz conditions on a nonlinear function, Krasnoselskii’s fixed point theorem (FPT) is used to prove the existence of a solution to the given problem. The uniqueness of the solution is established using Boyd and Wong’s FPT for nonlinear contractions. Moreover, the Ulam-Hyers and Ulam-Hyers-Rassias stability analyses for the solutions of \(\psi \) -HFIDE are also provided using Gronwall inequality. To illustrate the theoretical results, several examples are presented, confirming the practicality and effectiveness of the proposed approach.
