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Semilinear functional differential equations of fractional order with state-dependent delay

Benchohra M., Bennihi O., Ezzinbi K.

Commentationes Mathematicae

2013

Vol 53, No. 1

47--59

In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon- Granas type for contractions maps in Fr´echet spaces combined with -resolvent family is the main tool in our analysis.