New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS

By using a class of aggregation control functions, we introduce the concept multiple-HU-OS1-stability and get an optimum approximation for nonlinear single fractional differential equation (NS-ABC-FDE) with Mittag–Leffler kernel. We apply alternative fixed-point theorem to prove existence unique solution NS-ABC-FDE in symmetric matrix-valued FBS. Finally, example, show application obtained results.