Abstract
Mouffak BenchohraLaboratory of Mathematics,University of Sidi Bel Abbes,PO Box 89, 22000 Sidi BelAbbes, Algeria.benchohra@yahoo.comOmar BennihiD´epartement demath´ematiques etinformatique,Universit´e de Saida,20000, Saida, Alg´erie.obennihidz@yahoo.frKhalilEzzinbiD´epartement deMath´ematiques,Facult´e des Sciences,Semlalia, B.P.2390,Marrakech, Morocco.ezzinbi@ucam.ac.maABSTRACTIn this paper we provide sufficient conditions for the existence and uniqueness of mildsolutions for a class of neutral partial functional differential equations of fractionalorder with state-dependent delay. The nonlinear alternative of Frigon-Granas type forcontractions maps in Fr´echet spaces combined with α-resolvent family is the main toolin our analysis.RESUMENEn este art´iculo entregamos condiciones suficientes para la existencia y unicidad desolucionesmild parauna clase de ecuaciones diferencialesfuncionales parcialesneutralesde orden fraccionario con retraso dependiente del estado. La alternativa no lineal detipo Frigon-Granas para contracciones en espacios de F´echet combinados con familiasα-resolvente es la herramienta principal en nuestro an´alisis.Keywords and Phrases: Neutral functional differential equations; Riemman-Liouville fractionalderivative; mild solution; delay; fixed point; α-resolvent; Fr´echet space.2010 AMS Mathematics Subject Classification: 26A33; 34A08; 34K37.
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