In this paper, the concept of (α − ψ)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi b-metric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (α − ψ)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.