Fractional calculus theory includes the definitions of derivatives and integrals with arbitrary order.  This theory is used to solve some classes of differential equations and fractional differential equations. One of these equations is the damped free vibration equation. This equation is a linear homogeneous differential equation with constant coefficients. In this paper, we intend to solve this equation by means of N-fractional calculus method.

Fractional calculus theory includes the definitions of derivatives and integrals with arbitrary order.  This theory is used to solve some classes of differential equations and fractional differential equations. One of these equations is the damped free vibration equation. This equation is a linear homogeneous differential equation with constant coefficients. In this paper, we intend to solve this equation by means of N-fractional calculus method.