Aggregated multi-stability for a class of \(\mathfrak {J}\)-Hilfer fractional differential equations via Mittag-Leffler and hypergeometric type functions

Abstract

We propose a new concept of stability, called here as “aggregated multi-stability”, which is based on multiple aggregation functions and also uses Mittag-Leffler and hypergeometric functions. This is inspired by the general framework of the Ulam, Hyers and Rassias types of stability, but differs in essence both in the multi-dependency of various aggregation functions and in choosing special functions to play the role of controllers. This notion is applied here to a class of \(\mathfrak {J}\)-Hilfer fractional differential equations for which we identify sufficient conditions to guarantee its aggregated multi-stability.