Uniform error bounds are proved for the L1 scheme approximating the Caputo derivative in weighted Sobolev spaces with Muckenhoupt weights, yielding convergence for fractional ODE solvers.
Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation.SIAM Journal on Numerical Analysis, 55:1057–1079
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Error of discretization of Caputo fractional derivative in weighted spaces
Uniform error bounds are proved for the L1 scheme approximating the Caputo derivative in weighted Sobolev spaces with Muckenhoupt weights, yielding convergence for fractional ODE solvers.