Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used
Language
EN
Chapitre d'ouvrage
This item was published in
Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21). 2022-01p. 26-37
Springer International Publishing
English Abstract
The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a fractional model and if initial conditions are taken into account. The demonstration is done using ...Read more >
The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of fractional model analysis in which initial conditions are involved.Read less <
English Keywords
Fractional derivative
Caputo definition
Riemann-Liouville definition
Grünwald-Letnikov definition
Initial conditions
Memory