Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used

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 R...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 11318 - 11329
Main Authors SABATIER, Jocelyn, FARGES, Christophe
Format Journal Article
LanguageEnglish
Published AIMS Press 01.10.2021
Subjects
caputo definition
grünwald-letnikov definition
initial conditions
memory
riemann-liouville definition
time fractional derivative
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021657