TITLE:
Fourier Truncation Method for Fractional Numerical Differentiation
AUTHORS:
Ailin Qian, Jianfeng Mao
KEYWORDS:
Inverse Problems, Ill-Posed Problem, Fractional Numerical Differentiation, Fourier Regularization, Error Estimate
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.7,
July
15,
2011
ABSTRACT: We consider a ill-posed problem-fractional numerical differentiation with a new method. We propose Fourier truncation method to compute fractional numerical derivatives. A Holder-type stability estimate is obtained. A numerical implementation is described. Numerical examples show that the proposed method is effective and stable.