Fourier Series in Fractional Dimensional Space

Ali Dorostkar; Ahmad Sabihi

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arXiv · 2212.00049

Fourier Series in Fractional Dimensional Space

Ali Dorostkar·Ahmad Sabihi

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Abstract

In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. 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.

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BibTeX RIS

Ali Dorostkar, Ahmad Sabihi. 2022-12-01. Fourier Series in Fractional Dimensional Space. https://arxiv.org/abs/2212.00049

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