Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation

• Main Authors: Liu, Wenjie, Wang, Li-Lian, Wu, Boying
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Optimal Estimates; Fractional Taylor Formula
• Online Access: https://hdl.handle.net/10356/160560
• Institution: Nanyang Technological University

We present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and “interpolates” the usual Taylor formulas with two consecutive integer orders. This enables us to obtain an analogous formula for the Legendre expansion coeff...