Open ErikQQY opened 2 years ago
It seems the paper for the Fractional Derivative based on Chebyshev Polynomial need further check, especially for how it obtain the Cheybshev coefficients in equation (15) in paper https://doi.org/10.1016/j.entcs.2008.12.077.
The better Chebyshev Polynomial derivation may refer to the paper: https://d-nb.info/1171325665/34
I would also suggest including fractional derivatives by spectral methods, i.e. $$\partial_{t}^{\alpha} f(t) = \mathscr{F}^{-1}\left\lbrace{}(i \omega)^{\alpha}\mathscr{F}\left\lbrace{}f\right\rbrace{}\right\rbrace$$ This could leverage some neat julia FFT libraries. I've seen a MATLAB implementation for this kind of thing some years ago.
@LeeLizuoLiu Thanks for your suggestions! I will check the better Chebshev polynomial derivations in that paper😄
@pedromxavier Thanks for you suggestions on adding new algorithms to this package, and it would be nice if you can help implement Fourier spectral methods for evaluating fractional order derivatives.😆
@ErikQQY This one seems neat to warm up on spectral fracdiff: https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02590-4
This issue would be used to record algorithms need to be implemented.