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Abstract

The equation of motion for a driven fractional oscillator is formulated by replacing the classical second-order time derivative with a Caputo fractional derivative of order   In this study, the Sumudu transform method is employed to obtain an analytical solution of the fractional differential equation. By utilizing the integral properties of the Sumudu transform, which are adapted for Caputo fractional derivatives, the system’s response is explicitly derived in the time domain. The dynamic characteristics and phase plane trajectories of the fractional oscillator are analyzed for various values of  . The results demonstrate that the Sumudu transform provides an effective and accurate framework for analyzing the complex behavior of fractional oscillatory systems.