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Stability regions for linear fractional differential systems and their discretizations. (English) Zbl 1288.34005
Summary: This paper concerns with basic stability properties of linear autonomous fractional differential and difference systems involving derivative operators of the Riemann–Liouville type. We derive stability regions for special discretizations of the studied fractional differential systems including a precise description of their asymptotics. Our analysis particularly shows that discretizations based on backward differences can retain the key qualitative properties of underlying fractional differential systems. In addition, we introduce the backward discrete Laplace transform and employ some of its properties as the main proof tool.

MSC:
34A08 Fractional ordinary differential equations
34A30 Linear ordinary differential equations and systems
34D20 Stability of solutions to ordinary differential equations
39A12 Discrete version of topics in analysis
44A10 Laplace transform
65L12 Finite difference and finite volume methods for ordinary differential equations
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