Existence and blow-up of solutions for fractional wave equations of Kirchhoff type with viscoelasticity

<p style='text-indent:20px;'>In this paper, we deal with the initial boundary value problem of following fractional wave equation Kirchhoff type</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} u_{tt}+M([u]_{\alpha, 2}^2)(-\Delta)^{\alpha}u+(-\Delta)^{s}u_{t} = \int_{0}^{t}g(t-\tau)(-\Delta)^{\alpha}u(\tau)d\tau+\lambda|u|^{q -2}u, \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ M:[0, \infty)\rightarrow (0, \infty) $\end{document}</tex-math></inline-formula> is a nondecreasing and continuous function, id="M2">\begin{document}$ [u]_{\alpha, 2} Gagliardo-seminorm id="M3">\begin{document}$ u $\end{document}</tex-math></inline-formula>, id="M4">\begin{document}$ (-\Delta)^\alpha id="M5">\begin{document}$ (-\Delta)^s are Laplace operators, id="M6">\begin{document}$ g:\mathbb{R}^+\rightarrow \mathbb{R}^+ positive nonincreasing function id="M7">\begin{document}$ \lambda parameter. First, local global existence solutions obtained by using Galerkin method. Then nonexistence discussed via blow-up analysis. Our results generalize improve existing in literature.</p>