On a class of Kirchhoff problems with nonlocal terms and logarithmic nonlinearity

In this present paper, we concern investigating nonlinear Kirchhoff-type problems subject to Dirichlet boundary conditions, incorporating nonlocal terms and logarithmic nonlinearity in the \(\phi \) $\varphi$ -Hilfer fractional spaces with the \(\eta (\cdot )\) $\eta (·)$ -Laplacian operator by means of the do Mountain Pass Theorem, Fountain Theorem and Dual Fountain Theorem.