In this paper, we investigate the generalized Langevin-Sturm-Liouville differential problems involving Caputo-Atangana-Baleanu fractional derivatives of higher orders with respect to another positive, increasing function denoted by $\rho$. The fixed point theorems in the framework of Kransnoselskii and Banach are utilized to discuss the existence and uniqueness of the results. In addition, the stability criteria of Ulam-Hyers and generalize Ulam-Hyers are investigated by non-linear analysis besides fractional calculus. Finally, illustrative examples are reinforced by tables and graphics to describe the main achievements.
