Fractional integration: A comparative analysis of fractional integrators

The fractional integrator is certainly the key operator of fractional calculus, because of its fundamental applications in Fractional Differential Equation simulation and for the definition of fractional initial conditions. Fractional integration is defined by the classical Riemman-Liouville integral, derived from repeated integration. Three approaches commonly used to define the fractional integration operator (frequency method, frequency distributed model, Grünwald derivative) are analysed and compared in this paper.