This article investigates a type of hyperbolic equation of the fractional Kirchhoff with viscoelastic and logarithmic nonlinear terms subject to homogeneous Dirichlet-boundary:

$$\{\begin{array}{ll}{u}_{tt}+M([u{]}_s^2)(-\mathrm{\Delta }{)}^{s}u-{\int }_0^{t}g(t-\tau )(-\mathrm{\Delta }{)}^{s}u(\tau )d\tau +u_t=|u{|}^{h-2}u\ln |u|,& \text{in}\mathrm{\Omega }\times (0,\mathrm{\infty }),\\ u(\cdot ,0)=u_0,u_t(\cdot ,0)=u_1,& \text{in}\mathrm{\Omega },\\ u(\cdot ,t)=0,& \text{on}\mathrm{\partial }\mathrm{\Omega }\times (0,\mathrm{\infty }),\end{array}$$

where $[u{]}_s$ is the Gagliardo semi-norm of $u,$ $(-\mathrm{\Delta }{)}^s$ is the fractional Laplacian with $s\in (0,1)$, $2<2\gamma <h<2_s^{\ast }$, $u_0$ and $u_1$ are the initial functions, and $\mathrm{\Omega }\subset {\mathbb{R}}^N$ is a bounded domain with a smooth boundary. First, the global existence of solutions is established by combining the Galerkin method with the potential well theory. Subsequently, the finite-time blow-up of solutions is derived via the concavity method and a series of peculiar inequalities.

This article investigates a class of hyperbolic equations of the fractional Kirchhoff type with viscoelastic and nonlinear terms:

$$\{\begin{array}{l}{u}_{tt}+M([u{]}_s^2)(-\mathrm{\Delta }{)}^{s}u-{\int }_0^{t}g(t-\tau )(-\mathrm{\Delta }{)}^{s}u(\tau )d\tau +|u_t{|}^{a-2}{u}_t+u_t+u=|u{|}^{b-2}u,\\ \text{in}\mathrm{\Omega }\times (0,T),\\ u(x,t)=0,\text{on}\mathrm{\partial }\mathrm{\Omega }\times (0,T),\\ u(x,0)=u_0(x),u_t(x,0)=u_1(x)\text{in}\mathrm{\Omega },\end{array}$$

where $[u{]}_s$ is the Gagliardo semi-norm of $u$, $\mathrm{\Omega }\subset {\mathbb{R}}^N$ is a confined area featuring a smooth boundary, $(-\mathrm{\Delta }{)}^s$ is the fractional Laplacian with $s\in (0,1)$, $2<a<2\gamma <b<2_s^{\ast }$, $u_0$ and $u_1$ are the initial function. First, we obtain the existence of global solutions by combining the potential wells with the Galerkin method. Moreover, employing the perturbed energy approach, we systematically study the asymptotic behavior of solutions.