In this paper, we introduce the notion of s,r-contractive multivalued weakly Picard operators via simulation functions, named as Zs,r-contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. The well-posedness for such operators is also considered. Moreover, we generalize the results of Moţ and Petruşel. To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.