Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 10 (2015), 49 -- 59

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L1-SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR IMPLICIT FRACTIONAL ORDER DIFFERENTIAL EQUATIONS

Mouffak Benchohra and Mohammed Said Souid

Abstract. The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem.

2010 Mathematics Subject Classification: 26A33; 34A08.
Keywords: Implicit fractional-order differential equation; boundary value problem; Caputo fractional derivative; existence fixed point.

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Mouffak Benchohra Mohammed Said Souid
Laboratory of Mathematics, Département de Science Economique,
University of Sidi Bel Abbès, Université de Tiaret,
PO Box 89, Sidi Bel Abbès 22000, Algeria. Tiaret, Algérie.
and E-mail: souimed2008@yahoo.com
Department of Mathematics,
King AbdulazizUniversity
P.O. Box 80203, Jeddah 21589, Saudi Arabia.
E-mail: benchohra@univ-sba.dz

http://www.utgjiu.ro/math/sma