In this paper, we establish some fixed point results for α-λ-contractions in the class of quasi b-metric spaces. To illustrate the obtained results, we provide some examples and an application on a solution of an integral equation. We also study the stability of Ulam-Hyers and well-posedness of a fixed point problem. Our obtained results give an answer to an open problem of Kutbi and Sintunavarat (Abstr. Appl. Anal. 2014:268230, 2014 ).