A Plea for the Integration of Fractional Differential Systems: The Initial Value Problem

The usual approach to the integration of fractional order initial value problems is based on Caputo derivative, whose conditions are used formulate classical integral equation. Thanks an elementary counter example, we demonstrate that this technique leads wrong free-response transients. solution fundamental problem use frequency-distributed model integrator and its distributed conditions. Using model, solve previous example propose a methodology which generalization integer approach. Finally, applied modeling Fractional Differential Systems (FDS) formulation their transients in linear case. Two expressions derived, one using Mittag–Leffler function new definition exponential function.