J. Nonl. Evol. Equ. Appl. 2018 (2), pp. 11-24, published on Dec 25, 2018

Coupled Systems of Hilfer Fractional Differential Equations with Maxima

S. Abbas

Laboratory of Mathematics, University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria

M. Benchohra, J. E. Lazreg

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

G. N’Guérékata

Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA

Received on February 6, 2018, Revised version on April 19, 2018
Accepted on April 20, 2018

Communicated by Martin Bohner

Abstract.  In this paper, by applying Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness, we present some results concerning the existence of weak solutions for some coupled systems of Hilfer fractional differential equations with maxima.
Keywords:Differential equation with maxima; left-sided mixed Pettis-Riemann-Liouville integral of fractional order; Hilfer fractional derivative; coupled system; weak solution; fixed point.
2010 Mathematics Subject Classification:   26A33.

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