Error analysis of a backward L2 method on graded meshes for linear and semilinear subdiffusion equations

Time-fractional linear and semilinear parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are considered. Their solutions exhibit an initial singularity of type $t^σ$ for any fixed $σ\in (0,1) \cup (1,2)$. A backward L2-type discrete fractional-derivative operator of order $3-α$ i