ADVANCES IN ANALYSIS OF CAPUTO FRACTIONAL-ORDER NONAUTONOMOUS SYSTEMS: FROM STABILITY TO GLOBAL UNIFORM ASYMPTOTIC STABILITY

Cong Wu ()
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Cong Wu: Institutes for Systems Genetics, Frontiers Science Center for Disease-related Molecular Network, West China Hospital, Sichuan University, Chengdu 610041, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-17

Abstract: In this work, we analyze various stability (from stability to global uniform asymptotic stability) of Caputo fractional-order nonautonomous systems (CFONSs). With f(t,x) being only continuous, it is proven that the Caputo fractional derivative (CFD) of a general Lyapunov function V (t,x(t)) along solutions is continuous and moreover, t0CD tαV (t,x(t))≤ ∂V (t,x) ∂t(t,x(t))t0CD tαt + ∂V (t,x) ∂x ⋅ f(t,x)(t,x(t)), on the maximal interval of existence (MIE) of x(t). This together with the continuation of solutions suffices to prove the various stability theorems for CFONSs that are as general as those for integer-order systems, and make them practically applicable. The work reduces the assumption on vector field functions f for stability analysis from continuously differentiable (CD) to only continuous, which advances existing results to a large extent. Finally, some derived results are applied to real examples with numerical simulations.

Keywords: Stability; Global Uniform Asymptotic Stability Caputo Fractional-Order Nonautonomous System; Continuation of Solution (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500924

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