A class of variable-order fractional \(p(\cdot)\)-Kirchhoff-type systems (Q2023011)

Summary: 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.