Conformable Classical Mechanics: a pedagogical review

In this work we present a formalism to describe the fractional Newtonian mechanics based in conformable fractional calculus. In this sense, a brief revision about integral and differential conformable calculus is implemented. In sequence, the conformable version to Lagrangian and Hamiltonian formalism are presented. As examples, the conformable harmonic oscillator and conformable wave equation are discussed. In all situations, usual results are obtained when we consider $\alpha =1$. An interesting result is that in the case $1-\alpha \ll 1$ the conformable harmonic oscillator behaves like usual harmonic oscillator with time dependent and dissipation term.

Keywords:
Fractional Calculus; Conformable Fractional Derivative; Fractional Classical Mechanics.