2021/05/01 by Cyril Belardinelli, Belardinelli, Cyril
Mathematics · #26A33 #46F10 #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2105.00276
openalex publication_date 2021/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such as e.g. the absence of a semigroup property. It is shown that the proposed definition is free from such drawbacks. In order to achieve such a generalization one has to work in the context of tempered distributions (generalized functions) where the concept works nicely. The last part of the article shows the possibility of defining fractional derivatives of periodic functions (Fourier series).