Error of discretization of Caputo fractional derivative in weighted spaces
Provides rigorous error analysis for a widely used numerical method in fractional calculus, addressing a gap for weighted spaces relevant to certain applications.
The paper establishes uniform error bounds for the L1 discretization of the Caputo fractional derivative for functions in weighted Sobolev spaces with Muckenhoupt weights, and demonstrates convergence of the L1 scheme for fractional ODEs with numerical verification.
We establish uniform error bounds of the L1 discretization of the Caputo fractional derivative of the function from the weighted Sobolev space with weight belonging to the Mucknenhoupt class. We present how our framework works for several examples of weight, which belong to the Muckenhoupt class. As and application, we show the convergence of the L1 scheme for the Fractional ODE. Finally, we verify the theoretical results with numerical illustrations.