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

• المؤلفون الرئيسيون: Liu, Wenjie, Wang, Li-Lian, Wu, Boying
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2022
• الموضوعات: Science::Mathematics; Optimal Estimates; Fractional Taylor Formula
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/160560

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...