Abstract The goal of this paper is to consider a new fuzzy differential system consisting of a fuzzy fractional differential inclusion combined with a variational inequality, which is called fuzzy fractional differential variational inequality (FFDVI). Such a model captures the desired features of both fuzzy fractional differential inclusions and fractional differential variational inequalities within the same framework. By employing the set-valued version of the Krasnoselskii fixed point theorem, an existence of solutions is obtained for the FFDVI under some mild conditions. Moreover, an approximating algorithm is provided to find a solution of the FFDVI. Finally, two numerical examples are given to illustrate our main results.

中文翻译：

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一类由变分不等式驱动的模糊分数微分包含

摘要 本文的目的是考虑一种新的模糊微分系统，该系统由模糊分数阶微分包含与变分不等式相结合组成，称为模糊分数阶微分变分不等式（FFDVI）。这样的模型在同一框架内捕获了模糊分数阶微分包含和分数阶微分变分不等式的所需特征。通过采用Krasnoselskii不动点定理的集合值版本，在一些温和条件下获得了FFDVI解的存在性。此外，提供了一种近似算法来找到 FFDVI 的解决方案。最后，给出了两个数值例子来说明我们的主要结果。