Fundamentals of Fractional-order Systems

Abstract

Essentially, the mathematical problem for defining fractional-order derivatives and integrals consists of the following [2,7]: to establish, for each function f(z), z = x + jy of a general enough class, and for each number α (rational, irrational or complex), a correspondence with a function $g(z) = \mathcal{D}^{\alpha}_{c} f(z)$ fulfilling the following conditions.