J. Nonl. Evol. Equ. Appl. 2019 (5), pp. 81-94, published on February 14, 2020:

Existence and uniqueness results for nonlinear implicit fractional systems

S. Abbas

Laboratory of Mathematics, Geometry, Analysis, Control and Applications, Tahar Moulay University of Sa ̈ıda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria

M. Benchohra

Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

S. Bouriah

Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, P.O. Box 151 Chlef 02000, Algeria

J. Henderson

Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA

Received on February 27, 2018, revised version on March 20, 2019
Accepted on March 14, 2019 (with modifications)

Communicated by Martin Bohner

Abstract.  In this paper, we establish some existence and uniqueness results for a class of fractional dynamical systems with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem. An illustrative example is included to show the applicability of our results.
Keywords:Implicit fractional differential equation, existence, uniqueness, fixed point.
2010 Mathematics Subject Classification:   26A33.

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