Existence of Solutions for a Singular Double Phase Kirchhoff Type Problems Involving the Fractional q(x, .)-Laplacian Operator

In this paper, we consider a class of fractional Laplacian problems involving fractional \(q_{i}(x)\) $q_i(x)$ -laplacian operators \( (i=1:2)\) $(i=1:2)$ , and a singular nonlinearity. By using variational methods and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces, we prove the existence of solutions for such problems. An illustrative example is presented to validate the main results of this paper.