How to impose physically coherent initial conditions to a fractional system?

Autor:	Jocelyn Sabatier, Rachid Malti, Alain Oustaloup, Mathieu Merveillaut
Rok vydání:	2010
Předmět:	Numerical Analysis Diffusion (acoustics) Partial differential equation Diffusion equation Applied Mathematics Fractional-order system Mathematical analysis Initialization Fractional calculus Integer Modeling and Simulation Applied mathematics Representation (mathematics) Mathematics
Zdroj:	Communications in Nonlinear Science and Numerical Simulation. 15:1318-1326
ISSN:	1007-5704
DOI:	10.1016/j.cnsns.2009.05.070
Popis:	In this paper, it is shown that neither Riemann–Liouville nor Caputo definitions for fractional differentiation can be used to take into account initial conditions in a convenient way from a physical point of view. This demonstration is done on a counter-example. Then the paper proposes a representation for fractional order systems that lead to a physically coherent initialization for the considered systems. This representation involves a classical linear integer system and a system described by a parabolic equation. It is thus also shown that fractional order systems are halfway between these two classes of systems, and are particularly suited for diffusion phenomena modelling.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bf93a102820c2be4c7dde663a5b8d03b https://doi.org/10.1016/j.cnsns.2009.05.070 Zobrazit plný text záznamu Full Text from ScienceDirect