In this paper, we examine the existence and multiplicity of least energy solutions to a fractional Kirchhoff problem with logarithmic nonlinearity, given by the equation: \(\begin{aligned} \big \Vert \textbf{D}_{0^{+}}^{\gamma ,\kappa ;\Im }u\big \Vert _{p}^{(\vartheta -1)p}\;\textbf{L}^{\gamma ,\kappa ,\Im }_p u=h(\varsigma )|u|^{\vartheta p-2} u \log (|u|)+\xi |u|^{q-2} u, \quad \varsigma \in \mathfrak {Q}, \quad u=0 \quad \varsigma \in \partial \mathfrak {Q}, \end{aligned}\) where \(\mathfrak {Q}\) is a bounded domain in \(\mathbb {R}^{N}\) (with \(N\ge 2)\) that has a Lipschitz boundary, \(\vartheta \ge 1\) , h is a function that changes sign, continuous over \(\bar{\mathfrak {Q}}\) , \(\xi \) is a positive parameter, and \(q\in (1,{p}^{\star }_\gamma )\) . The equation employs the \(\Im \) -Hilfer fractional derivative with a p-Laplacian operator. Addressing the complications introduced by the logarithmic nonlinearity, we use the Nehari manifold minimization approach and establish a key estimate for the logarithmic term, which is vital for analyzing the energy functional’s properties. Our findings provide new insights into Kirchhoff-logarithmic problems and \(\Im \) -Hilfer generalized fractional differential equations with Dirichlet boundary conditions.
