关键词: Atangana-Baleanu分数阶导数, 分数阶模糊微分变分不等式, Krasnoselskii不动点定理, 解的存在性

Abstract: We considered a class of dynamic fuzzy systems, which consisted of fuzzy Atangana-Baleanu fractional differential inclusion and variational inequalities, called fuzzy fractional differential variational inequalities (FFDVI). It included the two fields of fuzzy fractional differential inclusion and variational inequalities, expanding the researchable problems in fuzzy environments. The model captured the desired features of the fuzzy fractional differential inclusion and fractional differential variational inequalities within the same framework. By using Krasnoselskii fixed point theorem, the existence of solutions of FFDVI under some mild conditions was obtained.

Key words: Atangana-Baleanu fractional derivative, fractional fuzzy differential variational inequality, Krasnoselskii fixed point theorem, existence of solution