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A New Look at the Initial Condition Problem

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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.

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

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Caputo derivative FARMA fractional derivative initial conditions linear systems Riemann-Liouville derivative Computer Science (miscellaneous) General Mathematics Engineering (miscellaneous)

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