Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

A reaction-diffusion problem with a Caputo time derivative of order $\alpha\in (0,1)$ is considered. The solution of such a problem is shown in general to have a weak singularity near the initial time $t=0$, and sharp pointwise bounds on certain derivatives of this solution are derived. A new analys... View More