Introduction to the techniques of the fractional calculus to investigate some models of the mathematical physics (in Portuguese)

TL;DR

This paper demonstrates the effectiveness of Laplace transform methods in solving fractional differential equations, highlighting their advantages in modeling physical systems like viscoelasticity and oscillators for improved accuracy.

Contribution

It introduces fractional calculus techniques for physical models, showing how Laplace transforms facilitate solving fractional differential equations in physics.

Findings

Fractional calculus effectively models viscoelastic and oscillator systems.

Laplace transform methods improve solution efficiency for fractional equations.

Fractional models offer more accurate predictions aligned with experimental data.

Abstract

In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible generalizations of certain physical problems in linear viscoelasticity and harmonic oscillators, proving that fractional calculus is well suited for the modelling and solving of problems usually treated by ordinary integer calculus, with the promissing advantages of being able to provide more accurate theoretical predictions to fit with experimental data. OBS: Article in portuguese accepted for publication at RBEF (Revista Brasileira de Ensino de F\'isica).