Čermák, Jan; Kisela, Tomáš; Nechvátal, Luděk Stability regions for linear fractional differential systems and their discretizations. (English) Zbl 1288.34005 Appl. Math. Comput. 219, No. 12, 7012-7022 (2013). 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. Cited in 26 Documents 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 Keywords:fractional differential system; fractional difference system; asymptotic stability; Laplace transform PDFBibTeX XMLCite \textit{J. Čermák} et al., Appl. Math. Comput. 219, No. 12, 7012--7022 (2013; Zbl 1288.34005) Full Text: DOI