A class of fractional p()-Kirchhoff type systems

TL;DR

This paper investigates a novel class of elliptic Kirchhoff systems involving variable-order fractional p(x)-operators, establishing existence results using variational methods, and extends previous work to more general variable exponent cases.

Contribution

Introduces the first study of Kirchhoff systems with variable-order fractional p(x)-operators, extending existing theories to variable exponents and fractional orders.

Findings

Existence of weak solutions established

Extension of previous results to variable-order fractional systems

Application of variational methods and Ekeland principle

Abstract

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.