In this article we introduce the notion of fuzzy measure of noncompactness. We define the fuzzy condensing and fuzzy k-set contractions using fuzzy measure of noncompactness. An extension of Stanislaw Szulfa’s fixed point theorem for a self-operator on a closed bounded and convex subset of a Banach space has been proved. Using the defined multivalued k-set contractions, generalizations of Kakutani-Fan and Krasnoselskii type theorems have been proved. For applications the existence result for solutions of a fractional Caputo-Fabrizio anti-periodic boundary value problem has been proved. We give some examples to validate our results.
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