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    Finite-time stability of mild solution to time-delay fuzzy fractional differential systems under granular computing
    (Springer Nature, 2022) Dong, Nguyen Phuong; Son, Nguyen Thi Kim; Allahviranloo, Tofigh; Tam, Ha Thi Thanh
    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. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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    State feedback control for fractional differential equation system in the space of linearly correlated fuzzy numbers
    (Elsevier, 2022) Son, Nguyen Thi Kim; Thao, Hoang Thi Phuong; Allahviranloo, Tofigh; Long, Hoang Viet
    In this paper, we will introduce Caputo fractional LC derivative defined in the linear correlated fuzzy-valued number space RF (A) and some of its applications, specifically the feedback control problem in the space RF (A) in the sense of Caputo fractional LC derivative. Firstly, we give definition of the Riemann-Liouville-LC integral and the Caputo fractional LC derivative of a function that takes value in RF (A). Besides, some Caputo factional LC derivative properties of the sum and difference of two functions have also been proved. Moreover, the problem of dynamic systems in space RF (A) is given in both cases where A is a symmetric or non-symmetric fuzzy number. Along with that, the stability theorems of the equilibrium point are also taken into consideration. Finally, we are interested in building a state feedback control function for the fractional differential equation system in space RF (A) to ensure the equilibrium point of the system is asymptotically stable