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