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Stability of nonlinear \(h\)-difference systems with \(n\) fractional orders. (English) Zbl 1340.39029

Summary: We study the stability of systems of \(h\)-difference equations of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with \(n\) fractional orders. Equivalent descriptions of fractional \(h\)-difference systems are presented. Sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with \(n\)-orders.

MSC:

39A30 Stability theory for difference equations
39A10 Additive difference equations
39A22 Growth, boundedness, comparison of solutions to difference equations
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