We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under δ-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples. © 2016 Uum et al., published by De Gruyter Open.