<p style='text-indent:20px;'>In this paper, we study fractional subdiffusion fourth parabolic equations containing Caputo and Caputo-Fabrizio operators. The main results of the paper are presented in two parts. For first part with derivative, focus on global local well-posedness results. We mild solution for biharmonic heat equation derivative case globally Lipschitz source term. A new we...

A Morley–Wang–Xu (MWX) element method with a simply modified right hand side is proposed for fourth order elliptic singular perturbation problem, in which the discrete bilinear form standard as usual nonconforming finite methods. The sharp error analysis given this MWX method. And Nitsche’s technique applied to MXW achieve optimal convergence rate case of boundary layers. An important feature s...