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 A compact difference scheme for fourth-order fractional sub-diffusion equations with Neumann boundary conditions Keywords:fourth-order fractional sub-diffusion equation, compact difference scheme, energy method Abstract: In this paper, a compact finite difference scheme with global convergence order $O(\tau^{2}+h^4)$ is derived for fourth-order fractional sub-diffusion equations subject to Neumann boundary conditions. The difficulty caused by the fourth-order derivative and Neumann boundary conditions is carefully handled. The stability and convergence of the proposed scheme are studied by the energy method. Theoretical results are supported by numerical experiments.