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

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DOI:

https://doi.org/10.4067/S0719-06462014000300004

Abstract

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 Fréchet spaces combined with α-resolvent family is the main tool in our analysis.

Keywords

Neutral functional differential equations , Riemman-Liouville fractional derivative , mild solution , delay , fixed point , α-resolvent , Fréchet space
  • Mouffak Benchohra Laboratory of Mathematics, University of Sidi Bel Abbes, PO Box 89, 22000 Sidi Bel Abbes, Algeria.
  • Omar Bennihi Département de mathématiques et informatique, Université de Saida, 20000, Saida, Algérie
  • Khalil Ezzinbi Département de Mathématiques, Faculté des Sciences, Semlalia, B.P.2390, Marrakech, Morocco.
  • Pages: 37-53
  • Date Published: 2014-10-01
  • Vol. 16 No. 3 (2014): CUBO, A Mathematical Journal

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Published

2014-10-01

How to Cite

[1]
M. Benchohra, O. Bennihi, and K. Ezzinbi, “Existence Results for Some Neutral Partial Functional Differential Equations of Fractional order with State-Dependent Delay”, CUBO, vol. 16, no. 3, pp. 37–53, Oct. 2014.

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