Fourier Series in Fractional Dimensional Space
General Mathematics
2022-12-02 v1 Functional Analysis
Abstract
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function . We call it fractional Fourier series of the order . Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.
Keywords
Cite
@article{arxiv.2212.00049,
title = {Fourier Series in Fractional Dimensional Space},
author = {Ali Dorostkar and Ahmad Sabihi},
journal= {arXiv preprint arXiv:2212.00049},
year = {2022}
}