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The BDF2 FDM for the fourth‐order equations with the multi‐term R‐L fractional integral kernels

In this paper, we formulated the finite difference method for the fourth order integro‐differential equation with the Riemann‐Liouville multi‐term fractional integral kernels. The formally two‐step backward differentiation formula method and second‐order convolution quadrature are used in time. The L2 and H1 ‐norm stability and convergence at each time level are given. Numerical results show that our scheme obtains the expected optimal convergence rates.