Extension of Lyapunov direct method about the fractional nonautonomous systems with order lying in $$\mathbf{(1,2)}$$(1,2)

In this paper, Lyapunov direct method is employed to study the stability problem of Caputo-type fractional nonautonomous systems with order between 1 and 2. By utilizing Riemann–Liouville fractional integral, some sufficient conditions on stability are derived. In the proof of the obtained results, Bellman–Gronwall’s inequality, the generalized Bihari inequality and estimates of Mittag-Leffler functions are employed. Besides, two examples and corresponding numerical simulations are provided to show the validity and feasibility of the proposed stability criterion.

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