Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 9 (2014), 79 -- 92

EXISTENCE RESULTS FOR NONLINEAR IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS

Mouffak Benchohra and Jamal Eddine Lazreg

Abstract. In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder' fixed point theorem and the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

2010 Mathematics Subject Classification: 26A33; 34A08.
Keywords: Initial value problem; Caputo's fractional derivative; implicit fractional differential equations; fractional integral; existence, Gronwall's lemma; fixed point.

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Mouffak Benchohra
Laboratory of Mathematics, University of Sidi Bel-Abbès
P. O. 89, Sidi Bel-Abbès 22000, Algérie.
and
Department of Mathematics, King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia.
e-mail: benchohra@yahoo.com

Jamal Eddine Lazreg
Laboratory of Mathematics, University of Sidi Bel-Abbès
P. O. 89, Sidi Bel-Abbès 22000, Algérie.
e-mail: lazregjamal@yahoo.fr

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