An introduction to fractional calculus and its Applications in Electric Circuits

Abstract A natural extension of differential calculus, initially proposed by l'Hôpital in a letter to Leibniz, leaded to the concept of fractional order derivatives. The application of fractional derivatives allows one to correctly describe the dynamics of many real systems, from biosystems to financial markets, where memory effects, dissipation and fractal dimensionality are present. This paper aims to present an overview of fractional derivatives and its representations, both in the form of Grünwald-Letnikov finite differences as well as in the form of Riemann-Liouville integrals, and to apply it in describing RC and RL electrical circuits of fractional order.