Twist of fractional oscillations

Abstract

Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived.

12 pages, 2 figures

References in corpus (1)

• Fractional oscillator

Cited by in corpus (4)

• Review of Some Promising Fractional Physical Models
• Hamiltonian formalism of fractional systems
• Long-term memory contribution as applied to the motion of discrete dynamical systems
• Fractional Powers of Derivatives in Classical Mechanics