Abstract
The purpose of this work is to investigate
the existence of solutions for a system of random differential equations involving
the Riemann–Liouville fractional derivative.
The existence result is established by means of a random abstract formulation to
Sadovskii’s fixed point theorem principle
[A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer,
Random semilinear system of differential equations with impulses,
Fixed Point Theory Appl. 2017 2017, Paper No. 27]
combined with a technique based on vector-valued metrics and
convergent to zero matrices. An example is also provided to illustrate our result.