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

Abstract

In this work, we analyze various stability (from stability to global uniform asymptotic stability) of Caputo fractional-order nonautonomous systems (CFONSs). With [Formula: see text] being only continuous, it is proven that the Caputo fractional derivative (CFD) of a general Lyapunov function [Formula: see text] along solutions is continuous and moreover, [Formula: see text] on the maximal interval of existence (MIE) of [Formula: see text]. 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 [Formula: see text] 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.