This article examines a boundary value problem that includes the Caputo derivative of fractional-order \(\mu \in \left] 4,5\right]\) . Primarily, we find the corresponding integral equation and use it to explore the existence and uniqueness (E&U) of the solution by employing Banach’s fixed point theorem (FPT). Then we analyze the existence of at least one solution utilizing Schaefer’s FPT. Furthermore, we verify that the solution of the proposed problem exhibits Ulam–Hyers (UH) stability and generalized UH stability via nonlinear analysis. Lastly, we develop specific examples to explain and support our main results.
