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    Lyapunov functions to caputo fractional neural networks with time-varying delays

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    Date
    2018-05-09
    Author
    Agarwal, Ravi
    Hristova, Snezhana
    O’Regan, Donal
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    Cited 1 times in Scopus (view citations)
    
    Recommended Citation
    Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal (2018). Lyapunov functions to caputo fractional neural networks with time-varying delays. Axioms 7 (2),
    Published Version
    http://www.mdpi.com/2075-1680/7/2/30/pdf
    Abstract
    One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.
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    http://hdl.handle.net/10379/10135
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