Introducci\'on al C\'alculo Fraccional

TL;DR

This paper provides an introductory overview of fractional calculus, covering its history, fundamental functions, derivatives, transforms, and an application to fractional free fall, aimed at beginners.

Contribution

It compiles essential concepts, properties, and historical context of fractional calculus, serving as an educational resource for introductory courses.

Findings

Explains properties of gamma, beta, and Mittag-Leffler functions.

Details Riemann-Liouville and Caputo derivatives and their applications.

Includes an example of fractional free fall problem.

Abstract

The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives that existed before current definitions. Properties of the gamma function, beta function and the Mittag-Leffler function are presented, which are fundamental pieces in the fractional calculus. The basic properties of Riemann-Liouville and Caputo fractional derivatives are presented, as well as their implementation to different functions. It also presents the Laplace transform of a fractional operator and an application to the fractional free fall problem.