A New Look at the Initial Condition Problem

Abstract

Publisher Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland.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.publishersversionpublishe