A New Look at the Initial Condition Problem
Manuel Duarte Ortigueira
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.
Topics & Concepts
Laplace transformGeneralityMathematicsInitial value problemApplied mathematicsAutoregressive modelMathematical analysisCalculus (dental)StatisticsMedicinePsychologyDentistryPsychotherapistFractional Differential Equations SolutionsControl Systems and IdentificationIterative Methods for Nonlinear Equations