The Fractional Differential Equation with Riemann Derivative Versus the Classical Equation for a Damped Harmonic Oscillator

摘要

Over the recent years, from among new mathematical methods the fractional differential calculus arouses particularly big hope. Some scientists expect that the fractional calculus will enable new discoveries and offer a new perspective on the old well-known problems. The equations of the harmonic oscillator is fundamental for many theories and models in physics and mechanics, and their solutions in the classical calculus are very well known. Some scientists attempt to look at them in a different way by replacing the classical derivatives with fractional ones and creating a set of new fractional equations. The aim of the paper is comparison of the classical equation for a damped harmonic oscillator with the fractional differential equation especially with fractional Riemann derivative.