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

Mouffak Benchohra; Omar Bennihi; Khalil Ezzinbi

doi:10.4067/S0719-06462014000300004

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

Authors

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.

DOI:

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

Keywords:

Neutral functional differential equations, Riemman-Liouville fractional derivative, mild solution, delay, fixed point, Î±-resolvent, Fréchet space

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 Î±-resolvent family is the main tool in our analysis.

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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.