Abstract
In this work, a time-fractional biharmonic equation with a Caputo derivative of fractional order α∈(0,1) is considered, whose solutions exhibit a weak singularity at initial time t=0. For this problem, a system of two second-order differential equations is derived by introducing a intermediate variable p=−Δu, then discretised the system using the standard finite element method in space together with the L1 discretisation of Caputo derivative on graded mesh in time. The H1-norm stability result of the method is established, and then a sharp H1-norm local convergent result is presented. Finally, numerical experiments are provided to further verify our theoretical analysis for each fixed value of α.
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