Interpretation of Fractional Derivatives as Reconstruction from Sequence of Integer Derivatives

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Tarasov, Vasily E.^*

Affiliations: Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia. tarasov@theory.sinp.msu.ru

Correspondence: [*] Address for correspondence: Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie gory, GSP-1, Moscow 119991, Russian Federation

Abstract: In this paper, we propose an “informatic” interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders as reconstruction from infinite sequence of standard derivatives of integer orders. The reconstruction is considered with respect to orders of derivatives.

Keywords: Fractional derivative, Riemann-Liouville derivative, Caputo derivative, derivations of Hadamard type, sampling theorem

DOI: 10.3233/FI-2017-1502

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 431-442, 2017