  This paper is concerned with an elliptic system of Kirchhoff type, driven by
the variable-order fractional $p(x)$-operator. With the help of the direct
variational method and Ekeland variational principle, we show the existence of
a weak solution. This is our first attempt to study this kind of system, in the
case of variable-order fractional variable exponents. Our main theorem extends
in several directions previous results.

Analysis of PDEs