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 application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In particular, a result relating fractional dynamics to high frequency dielectric response is used as motivation. In addition 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.

arXiv comment12 pages, 11 figures

References in corpus (6)

• No Violation of the Leibniz Rule. No Fractional Derivative
• Review of Some Promising Fractional Physical Models
• Models of dielectric relaxation based on completely monotone functions
• Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
• The Hilbert transform: Applications to atomic spectra
• Universal Electromagnetic Waves in Dielectric