The main aim of this paper is to prove the existence and uniqueness of a fixed point for a class of cyclic contractions via simulation functions in the context of metric-like spaces. These results are generalizations of the recent results in [M. Jleli, B. Samet, An improvement result concerning fixed point theory for cyclic contractions, Carpathian J. Math., 32 (2016), 339-347]. We also prove a stability and well-posedness of a fixed point problem. Moreover, some examples and an application on the existence and uniqueness of solutions to a class of functional integral equations are given to support the obtained results.