Uniqueness and Ulam–Hyers Stability for Nonlinear Fractional Duffing Boundary Value Differential Equation

Abstract

This paper investigates uniqueness and Ulam-Hyers stability for nonlinear fractional Duffing boundary value problems involving sequential generalized Ψ -Prabhakar-Atangana-Baleanu-Caputo derivatives with cubic nonlinearity. Under appropriate Lipschitz conditions on the nonlinear forcing function, we establish uniqueness of solutions via Banach fixed point theorem. The contractivity condition L Ω1+3 Mδ R2 Ω1 +Ω2<1 is derived, where L is the Lipschitz constant and R is the solution bound. Ulam-Hyers and Ulam-Hyers-Rassias stability results are obtained through direct estimation techniques. Several corollaries for special parameter regimes and a detailed numerical example with comparative error analysis validate the theoretical framework.