American Institute of Mathematical Sciences

March  2020, 13(3): 853-865. doi: 10.3934/dcdss.2020049

Fractional input stability and its application to neural network

 Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Laboratoire Lmdan, BP 5683 Dakar Fann, Sénégal

* Corresponding author: Ndolane Sene

Received  June 2018 Revised  August 2018 Published  March 2019

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.

Citation: Ndolane Sene. Fractional input stability and its application to neural network. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 853-865. doi: 10.3934/dcdss.2020049
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References:
Not CICS and not BIBS
FIS of fractional neural network
Asymptotic stability of trivial $x = 0$ solution of FDE with a converging input
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