The Evolution of Fractional Calculus

Abstract

Fractional Calculus started in 1695 with Leibniz discussing the meaning of $D^ny$ for $n = 1/2$. Many mathematicians developed the theoretical concepts, but the area remained somewhat unknown from applied sciences. During the eighties FC emerged associated with phenomena such as fractal and chaos and, consequently, in nonlinear dynamical. In the last years, Fractional Calculus became a popular tool for the modeling of complex dynamical systems with nonlocality and long memory effects.