Error Estimates for Approximations of Time-Fractional Biharmonic Equation with Nonsmooth Data

We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order α∈ (0 , 1 ) and a locally Lipschitz continuous nonlinearity. Local and global existence of solutions is discussed and detailed regularity results are provided. A finite element method in space combined with a backward Euler convolution quadrature in time is analyzed. Our objective is to allow initial data of low regularity compared to the number of derivatives occurring in the governing equation. Using a semigroup type approach, error estimates of optimal order are derived for solutions with smooth and nonsmooth initial data. Numerical tests are presented to validate the theoretical results.