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In this paper, a compact finite difference scheme with global convergence order O(τ + h) 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.

A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS