Misconceptions in using Riemann-Liouville’s and Caputo’s definitions for the description and initialization of fractional partial differential equations

摘要

In this paper, it is shown that neither Riemann-Liouville’s nor Caputo’s definitions can be used to properly take into account initial conditions in the description of a fractional partial differential equation. This demonstration is done on a counterexample. Some suggestions are made to address this problem.