Existence and Ulam Type Stability for Impulsive Fractional Differential Systems with Pure Delay

Through literature retrieval and classification, it can be found that for the fractional delay impulse differential system, existence uniqueness of solution UHR stability system are rarely studied by using polynomial function matrix. In this paper, we firstly introduce a new concept impulsive delayed Mittag–Leffler type vector function, which helps us to construct representation an exact linear equations (IFDDEs). Secondly, Banach’s Schauder’s fixed point theorems, derive some sufficient conditions guarantee solutions nonlinear IFDDEs. Finally, obtain Ulam–Hyers (UHs) Ulam–Hyers–Rassias (UHRs) class