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

Nassim Guerraiche, Samira Hamani, and Johnny Henderson

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


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