{'fraction_non_alphanumeric': 0.02386634844868735, 'fraction_numerical': 0.002386634844868735, 'mean_word_length': 5.766129032258065, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lyapunov functions for fractional‐order nonlinear systems with Atangana–Baleanu derivative of Riemann–Liouville type

Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order 0 < α < 1 modeled by the Atangana–Baleanu derivative of Riemann–Liouville type (ABR), which allows consistent modeling of a large class of physical systems with complex dynamics. The main contribution of the paper consists of some novel inequalities for the Atangana–Baleanu derivative of the Riemann–Liouville type. Furthermore, the proposed study allows considering both quadratic and convex Lyapunov functions to analyze stability in ABR systems by applying the Direct Lyapunov Method.