The Fractional Harmonic Oscillator: Analysis and Computation

Abstract

This thesis explores the fractional harmonic oscillator by extending classical models with fractional derivatives. Analytical and numerical methods, such as Laplace transforms and L1/L2 schemes, are used to study memory and damping effects. The results reveal non-local behavior in oscillations and suggest extensions to nonlinear systems like the Van der Pol and Lotka–Volterra models.