An introduction to fractional calculus: Numerical methods and application to HF dielectric response

Abstract

The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its applications to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In partic-ular, a result connecting fractional dynamics to high frequency dielectric response is used as motivation. In addi-tion to the theoretical discussion, a comprehensive review of two numerical procedures for fractional integration is carried out, allowing one immediately to build numerical models applied to high frequency electromagnetics and correlated fields.