Fractional order differential switched systems with coupled nonlocal initial and impulsive conditions

Abstract

In this paper, we discuss a new class of fractional order differential switched systems with coupled nonlocal initial and impulsive conditions in Rn. We firstly derive a solution formula for this system. Secondly, we utilize three well-known fixed point methods to present the existence results. Moreover, we use Schauder topological degree theory to show a new existence result for resonant case: Landesman–Lazer conditions. Finally, we introduce the concepts of Ulam's type stability and present new stability results in the space of fractional version piecewise continuous functions.