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

Abstract

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.

Keywords

• time fractional derivative
• caputo definition
• riemann-liouville definition
• grünwald-letnikov definition
• initial conditions
• memory