Fractional order differential switched systems with coupled nonlocal initial and impulsive conditions. (English) Zbl 1387.34012
Summary: In this paper, we discuss a new class of fractional order differential switched systems with coupled nonlocal initial and impulsive conditions in \(\mathbb{R}^n\). 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’s 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.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A36 | Discontinuous ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B37 | Boundary value problems with impulses for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fractional-order differential switched systems; nonlocal impulsive conditions; solutions; existence; stabilityReferences:
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