Eur. Phys. J. Special Topics 226, 3525–3549 (2017)
https://doi.org/10.1140/epjst/e2018-00029-y

Regular Article

Random solutions to a system of fractional differential equations via the Hadamard fractional derivative

¹ Laboratory of Mathematics, University of Sidi Bel Abbés, P.O. Box 89, 22000 Sidi-Bel-Abbés, Algeria
² Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA

^a e-mail: agh_ouahab@yahoo.fr

Received: 8 June 2017
Published online: 25 July 2018

Abstract

In this work, we use a new random fixed point theorem in vector metric spaces due to Sinacer et al. [M.L. Sinacer et al., Random Oper. Stoch. Equ. 24, 93 (2016)] to prove the existence of solutions and the compactness of solution sets of a random system of fractional differential equations via the Hadamard-type derivative. The existence, modification and stochastically continuity of an M²-solution are also proved.