Electron. J. Differential Equations, Vol. 2016 (2016), No. 324, pp. 1-10.

Nonlinear implicit differential equations of fractional order at resonance

Mouffak Benchohra, Soufyane Bouriah, John R. Graef

Abstract:
In this article, we obtain an existence result for periodic solutions to nonlinear implicit fractional differential equations with Caputo fractional derivatives. Our main tools is coincidence degree theory, which was first introduced by Mawhin. Also we present two examples to show the applicability of our results.

Submitted July 25, 2016. Published December 21, 2016.
Math Subject Classifications: 34A08, 34B15.
Key Words: Caputo's fractional derivative; fractional integral; existence; implicit fractional differential equations; periodic solutions; coincidence degree theory.

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Mouffak Benchohra
Laboratory of Mathematics
University of Sidi Bel-Abbes, P.O. Box 89
Sidi Bel-Abbes 22000, Algeria
email: benchohra@univ-sba.dz
Soufyane Bouriah
Laboratory of Mathematics
University of Sidi Bel-Abbes, P.O. Box 89
Sidi Bel-Abbes 22000, Algeria
email: bouriahsoufiane@yahoo.fr
John R. Graef
Department of Mathematics
University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA
email: john-graef@utc.edu

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