On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type

We study for nonlinear Kirchhoff's model of pseudo parabolic type by considering its two different problems. style='text-indent:20px;'>\begin{document}$ \bullet $\end{document} For initial value problem, we obtain the results on existence and regularity solutions. Moreover, also prove that solutions \begin{document}$ u corresponding with id="M3">\begin{document}$ \beta < 1 problem convergence to id="M4">\begin{document}$ id="M5">\begin{document}$ = $\end{document}. id="M6">\begin{document}$ final show ill-posed property in sense Hadamard is occurring. Using Fourier truncation method regularize problem. We establish some stability estimates id="M7">\begin{document}$ H^1 id="M8">\begin{document}$ L^p norms under a-priori conditions sought solution.