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

✍ Scribed by Jocelyn Sabatier; Mathieu Merveillaut; Rachid Malti; Alain Oustaloup

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 436 KB
• Volume: 15
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2009.05.070

✦ Synopsis

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.