2022/12/01 by Ali Dorostkar, Dorostkar, Ali, Ahmad Sabihi +1
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #General Mathematics (math.GM) #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2212.00049
openalex publication_date 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function f(t;α). We call it fractional Fourier series of the order α. 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.