Existence Results for Some Neutral Partial Functional Differential Equations of Fractional order with State-Dependent Delay

• Mouffak Benchohra ^[1] ; Omar Bennihi ^[2] ; Khalil Ezzinbi ^[3]
  1. [1] University of Sidi Bel Abbes Laboratory of Mathematics
  2. [2] Université de Saida Département de mathématiques et informatique
  3. [3] Faculté des Sciences Semlalia Département de Mathématiques

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• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 3, 2014, págs. 37-53
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000300004
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  • Texto completo
• Resumen
  • español

    En este artículo entregamos condiciones suficientes para la existencia y unicidad de soluciones mild para una clase de ecuaciones diferenciales funcionales parciales neutrales de orden fraccionario con retraso dependiente del estado. La alternativa no lineal de tipo Frigon-Granas para contracciones en espacios de Fechet combinados con familias α-resolvente es la herramienta principal en nuestro análisis.

  • English

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

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