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

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.

Automated summary

In this paper, we apply n-ary aggregation functions to special functions to define a class of matrix-valued fuzzy controllers. These controllers help us study the Ulam-Hyers stability of (non)autonomous fractional differential systems in the Hilfer sense in matrix-valued fuzzy n-normed spaces. By using the properties of Mittag-Leffler functions, Laplace transform, and the non-standard Gronwall inequality, we propose efficient conditions for the (asymptotic) stability of the governing model in matrix fuzzy normed spaces.