Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 15, Issue 5, Pages 1318-1326Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2009.05.070
Keywords
Fractional order system; Diffusion equation; Initialization
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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. (C) 2009 Published by Elsevier B.V.
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