MATHEMATICAL TREATMENT OF OSCILLATORY SYSTEMS USING THE FRACTIONAL CALCULUS

Abstract

In this work, the fractional calculus methods are used to solve essential problems in conservative and non-conservative oscillatory systems. Regarding the non-conservative systems, the key factor is to modify the standard fractional Lagrange equations by including the fractional Rayleigh’s dissipation function with a time fractional derivative of the displacement. The results are tested by applying them to well known Oscillatory systems under conservative and non-conservative forces. The calculations reveal that, the equations of motion are controlled by the fractional order derivative (ï¡), as (ï¡) go of motion become as those for ordinary oscillatory systems.