Automatic initialization of the Caputo fractional derivative

Initialization of Riemann-Liouville and Caputo fractional derivatives remains an open research topic. These fractional derivatives are fundamentally related to fractional integration operators, so their initial conditions are the initial state vector of the associated fractional integrators. The paper is intended to propose an automatic initialization technique for practical calculation of the Caputo fractional derivative. Indirectly, this algorithm provides and efficient estimate of the initial state vector. Numerical simulations show the efficiency of the proposed initialization technique and provide interpretations of the long range memory phenomenon which is the main feature of fractional systems.