Solvability and convergence analysis of a transformed L1 finite difference scheme for TFMBE models without slope selection

This paper presents a transformed L1 finite difference method for the time-fractional molecular beam epitaxy (TFMBE) model without slope selection, taking the initial singularity of the solution into account. A novel discrete fractional Gronwall inequality is used to provide unconditionally optimum error estimates. The convergence results indicate that the method has an order of 2 in the spatial direction and an order of $ 2-\alpha $ 2-alpha in the temporal direction. Numerical experiments are carried out to corroborate our theoretical findings.