Open AccessInitial value problems should not be associated to fractional model descriptions whatever the derivative definition used
Author(s) -
Jocelyn Sabatier,
Christophe Farges
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021657
Subject(s) - counterexample , fractional calculus , mathematics , simple (philosophy) , derivative (finance) , field (mathematics) , value (mathematics) , calculus (dental) , pure mathematics , combinatorics , statistics , epistemology , philosophy , economics , medicine , dentistry , financial economics
The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time 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 time fractional model analysis in which initial conditions are involved.