Version 1
: Received: 12 October 2023 / Approved: 13 October 2023 / Online: 13 October 2023 (17:45:11 CEST)
Version 2
: Received: 17 March 2024 / Approved: 18 March 2024 / Online: 19 March 2024 (10:15:54 CET)
Version 3
: Received: 23 June 2024 / Approved: 24 June 2024 / Online: 25 June 2024 (16:42:14 CEST)
Version 4
: Received: 12 July 2024 / Approved: 15 July 2024 / Online: 15 July 2024 (13:44:54 CEST)
How to cite:
Diedrich, E. The Fourier Continuous Derivative: A New Approach to Fractional Differentiation. Preprints2023, 2023100913. https://doi.org/10.20944/preprints202310.0913.v1
Diedrich, E. The Fourier Continuous Derivative: A New Approach to Fractional Differentiation. Preprints 2023, 2023100913. https://doi.org/10.20944/preprints202310.0913.v1
Diedrich, E. The Fourier Continuous Derivative: A New Approach to Fractional Differentiation. Preprints2023, 2023100913. https://doi.org/10.20944/preprints202310.0913.v1
APA Style
Diedrich, E. (2023). The Fourier Continuous Derivative: A New Approach to Fractional Differentiation. Preprints. https://doi.org/10.20944/preprints202310.0913.v1
Chicago/Turabian Style
Diedrich, E. 2023 "The Fourier Continuous Derivative: A New Approach to Fractional Differentiation" Preprints. https://doi.org/10.20944/preprints202310.0913.v1
Abstract
The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
