In this work, our intention is to introduce the notion of rational (α-β-FG)-contraction mapping in b-metric-like spaces, and produce relevant fixed point and periodic point results for weakly α-admissible mappings. Ulam-Hyers stability of this problem is also investigated. To illustrate our results, we give throughout the paper some examples, in particular in order to justify the use of rational terms. As an application, we obtain sufficient conditions for the existence of solutions for Cantilever Beam Problem. © 2017, University of Nis. All rights reserved.