Multi-stability of non homogenous vector-valued fractional differential equations in matrix-valued Menger spaces

Abstract

In this paper, we apply some special functions (Mittag-Leffler, Gauss Hypergeometric, Bessel-Maitland and Fox H functions) to investigate a class of matrix-valued random control functions. Using this kind of control function helps us to introduce the concept of multi-stability and get an approximation of non homogenous vector-valued fractional differential equations via the fixed point method. Further, some Ulam-Hyers stability results for the mentioned fractional differential equations in different cases are obtained. Also, we determine some sufficient conditions for the stability of non homogenous vector-valued fractional differential equations.