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.

中文翻译：

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非紧实性的模糊测度及其在涉及非奇异核的分数次反周期边值问题中的应用

在本文中，我们介绍了非紧实度的模糊度量的概念。我们使用非紧致度的模糊度量来定义模糊凝聚和模糊k集收缩。证明了斯坦尼斯瓦夫·萨夫拉（Stanislaw Szulfa）不动点定理在Banach空间的封闭有界和凸集上的自算子的扩展。使用定义的多值k集压缩，证明了Kakutani-Fan和Krasnoselskii型定理的推广。对于应用，已经证明了分数Caputo-Fabrizio反周期边值问题解的存在结果。我们举一些例子来验证我们的结果。