Abstract
The stability of linear systems with the Caputo fractional-, variable-order difference operators of convolution type is investigated. We present the recurrence formula for the solution to linear initial value problems with the operator that is defined as the convex combination of two fractional-, variable-order difference operators. The conditions for asymptotic stability of considered equations are formulated and proven. Finally, some examples that illustrate our results are presented.
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The work was supported by Polish funds of National Science Center, granted on the basis of decision DEC-2016/23/B/ST7/03686.
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Mozyrska, D., Wyrwas, M., Oziablo, P. (2021). Asymptotic Stability of Fractional Variable-Order Discrete-Time Equations with Terms of Convolution Operators. In: Awrejcewicz, J. (eds) Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches. DSTA 2019. Springer Proceedings in Mathematics & Statistics, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-77310-6_18
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