3. Analysis of a New Stability on Matrix Valued Fuzzy Spaces

We apply the Radu-Miheţ method which is derived from an alternative fixed point theorem with a class of matrix-valued fuzzy controllers to approximate a fractional Volterra integrodifferential equation with \(\psi \)-Hilfer fractional derivative in matrix-valued fuzzy k-normed spaces to obtain an approximation for this type of fractional equations. Using a class of aggregation control functions, we introduce the concept of multiple-HU-\(OS_1\)-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers-Ulam-H-Fox stability for the conformable fractional differential equation with a constant coefficient. In a fuzzy environment, we introduce a matrix-valued fuzzy Wright controller class to investigate the Hyers–Ulam–Wright stability for the non-homogeneous fractional delay oscillation equation (NH-FD-O) with order \(\kappa \).