On physical interpretations of fractional integration and differentiation
type: Item
instance of: scholarly article
title: On physical interpretations of fractional integration and differentiation
zbMATH Open document ID: 0897.26002
DOI: 10.1007/BF02070871
published in: Theoretical and Mathematical Physics
publication date: 1998-03-01T00:00:00Z
review text: The paper deals with physical interpretation of fractional integration and differentiation in the Riemann-Liouville form [see Sections 2 and 6 in the book by \textit{S. G. Samko}, \textit{A. A. Kilbas} and \textit{O. I. Marichev}: ``Fractional integrals and derivatives: Theory and applications'' (Russian, 1987; Zbl 0617.26004; English translation, 1993; Zbl 0818.26003)]. The problem, when a fractional order system can be represented by a causal dynamic model, is under consideration. The known models of such a kind are discussed, and a new model is presented: fractional integration and differentiation are realized as the linear dynamical systems \[ {dz(x)\over dx}= A(x) z(x)+ Bh(x),\quad f(x)= C(x)z(x), \] and \[ {dz(x)\over dx}= P(x) z(x)+ Q(x) f(x),\quad h_n(x)= R(x) z(x)+ S(x) f(x), \] with \(x\) as a time variable, respectively. In this way, regularization of fractional integration and differentiation is studied, asymptotic error estimates and simulation results are given.
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 1120308
zbMATH Keywords: fractional integration and differentiation
zbMATH Keywords: linear dynamical systems
author: Roman S. Rutman
reviewed by: A. A. Kilbas
describes a project that uses: CRONE
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1120308