Initial value problems for fractional functional differential inclusions with Hadamard type derivative

Nassim Guerraiche, Samira Hamani, and Johnny Henderson

Address:
N. Guerraiche, S. Hamani Laboratoire des Mathematiques Appliquès et Pures, Universitè de Mostaganem, B.P. 227, 27000, Mostaganem, Algerie
J. Henderson, Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA

E-mail:
nassim.guerraiche@univ-mosta.dz
hamani_samira@yahoo.fr
johnny_henderson@baylor.edu

Abstract: We establish sufficient conditions for the existence of solutions of a class of fractional functional differential inclusions involving the Hadamard fractional derivative with order $\alpha \in (0,1]$. Both cases of convex and nonconvex valued right hand side are considered.

AMSclassification: primary 26A33; secondary 34A60.

Keywords: fractional differential inclusion, Hadamard-type fractional derivative, fractional integral, fixed point, convex.

DOI: 10.5817/AM2016-4-263