Mittag-Leffler String Stability of Singularly Perturbed Stochastic Systems within Local Fractal Space

The present paper tends to define a new type of string stability based on Mittag-Leffler function that is called (p alpha)-string stability. This kind of stability will be considered for a class of singularly perturbed stochastic systems of fractional order. The fractional derivative in these systems is situated in the local sense. String stability indicates uniform boundedness of the interconnected system, if the initial cases of interconnected system be uniformly bounded. The deduction of the sufficient conditions of stability is based on a mixture of the concept of the Mittag-Leffler stability with the notion of p-mean string stability of singularly perturbed stochastic systems. In this sense the objective, it is argued, is to investigate the full order system in their lower order subsystems, i.e., the reduced order system and the boundary layer correction.