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Abstract

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems.

Original languageEnglish
Article number1771
Number of pages17
JournalMathematics
Volume10
Issue number10
DOIs
Publication statusPublished - 23 May 2022

Keywords

  • Caputo derivative
  • FARMA
  • fractional derivative
  • initial conditions
  • linear systems
  • Riemann-Liouville derivative

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