Finite-time stability of mild solution to time-delay fuzzy fractional differential systems under granular computing

In this work, based on the concept of the granular Caputo fractional derivative, a class of fuzzy fractional differential systems with finite-time delay is investigated. We firstly introduce the concept of Mittag-Leffler type matrix function generated by a square fuzzy matrix. Then through Laplace transform, we construct the explicit formula of mild solutions to the problem. Applying Banach contraction principle, the existence and uniqueness of fuzzy mild solution of the problem are shown. Secondly, utilizing Jensen inequality, Hölder inequality and Gronwall inequality, we establish sufficient conditions to guarantee for finite-time stability results of the considered problem. Especially, these conditions are obtained without Lipschitz property of the function f containing delay term. Finally, we have also illustrated the theoretical results by an numerical example.