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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.3 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000300003 

CUBO A Mathematical Journal Vol.12, N° 03, (35–48). October 2010

 

Measure of Noncompactness and Nondensely Defined Semilinear Functional Differential Equations with Fractional Order

 

MOUFFAK BENCHOHRA1, GASTON M. N’GUÉRÉKATA AND DJAMILA SEBA

Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie email: benchohra@univ-sba.dz

Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA email: Gaston.N’Guerekata@morgan.edu

Département de Mathématiques, Université de Boumerdès, Avenue de l’indépendance, 35000 Boumerdès, Algérie email: djam_seba@yahoo.fr


ABSTRACT

This paper is devoted to study the existence of integral solutions for a nondensely defined semilinear functional differential equations involving the Riemann-Liouville derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

Key words and phrases: Partial differential equations, fractional derivative, fractional integral, fixed point, semigroups, integral solutions, finite delay, measure of noncompactness, fixed point, Banach space.


RESUMEN

Este artículo es dedicado al estudio de existencia de soluciones integrales para ecuaciones diferenciales funcionales semilineales envolviendo la derivada de Riemann-Liouville en un espacio de Banach. Los argumentos se basan en un teorema de punto fijo de Mönch y la técnica de no compacidad.

Math. Subj. Class.: 34G20, 34G25, 26A33, 26A42.


Notas

1Corresponding author

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