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Article Contents

# Fractional input stability and its application to neural network

• * Corresponding author: Ndolane Sene
• This paper deals with fractional input stability, and contributes to introducing a new stability notion in the stability analysis of fractional differential equations (FDEs) with exogenous inputs using the Caputo fractional derivative. In particular, we study the fractional input stability of FDEs with exogenous inputs. A Lyapunov characterization of this notion is proposed and several examples are provided to explain the fractional input stability of FDEs with exogenous inputs. The applicability and simulation of this method are illustrated by studying the particular class of fractional neutral networks.

Mathematics Subject Classification: Primary: 26A33, 93D05; Secondary: 93D25.

 Citation:

• Figure 1.  Not CICS and not BIBS

Figure 2.  FIS of fractional neural network

Figure 3.  Asymptotic stability of trivial $x = 0$ solution of FDE with a converging input

Figures(3)