Fractional Newton mechanics with conformable fractional derivative

In this paper we use the conformable fractional derivative and integral to discuss the fractional Newtonian mechanics. The fractional version of the calculus of variations is introduced and the fractional Euler–Lagrange equation is constructed. Some mechanical problems such as fractional harmonic oscillator problem, the fractional damped oscillator problem and the forced oscillator problem are discussed in the one-dimensional fractional dynamics.