The dynamic behavior of anti-periodic solutions for fractional-order inertia Cohen-Grossberg neural networks is investigated in the article. First, the fractional derivative with different orders is transformed to that with the same order by properly variable substitution; Second, a sufficient condition can ensure the solution is global Mittag-Leffler stability by using properties of fractional calculus and characteristics of Mittag-Leffler function; Moreover, a sufficient condition for the existence of an anti-periodic solution is given by constructing a system sequence solution that converges to a continuous function using Arzela-Asolitheorem. In the final, we verify the correctness of the conclusion by numerical simulation.
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<p>Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays are investigated in the article. We derive the relationship between the fractional-order integrals of the state function with and without delays through the division of time interval, using the properties of fractional calculus, and initial conditions. Moreover, by constructing the sequence solution of the system function which converges to a continuous function uniformly with the Arzela-Asoli theorem, a sufficient condition is obtained to ensure the existence of an anti-periodic solution and Mittag-Leffler stabilization of the system. In the final, we verify the correctness of the conclusion by numerical simulation.</p>
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The boundedness, global Mittag-Leffler stability (GMLS), and the S-asymptotic ω-periodic of fuzzy fractional-order inertial neural networks (FINN) with delays are discussed. Using the properties of Riemann-Liouville fractional-order calculus, variable substitutions and the property of fuzzy functions are adopted to get the boundedness, the GMLS, and S-asymptotic ω-periodic of the system. Furthermore, a numerical example is given to demonstrate the theorems.
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