Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
767402 | Communications in Nonlinear Science and Numerical Simulation | 2010 | 9 Pages |
Abstract
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.
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Authors
Jocelyn Sabatier, Mathieu Merveillaut, Rachid Malti, Alain Oustaloup,