Stability and controllability results by n–ary aggregation functions in matrix valued fuzzy n–normed spaces

Abstract

In the present paper, we apply the n–ary aggregation functions on several special functions (Hypergeometric function, generalized exponential function, and Fox's H –function) to define a class of matrix–valued fuzzy controllers which help us to study the Ulam–Hyers stability for a (non) autonomous fractional differential system in the Hilfer sense, through the fixed point theorem, in a matrix valued fuzzy n–normed space. Next, by the properties of Mittag-Leffler functions, the Laplace transform and the non–standard Gronwall inequality, we propose some efficient conditions on the (asymptotic) stability of the governing model, in matrix fuzzy normed spaces.

Topics & Concepts