A study of forced oscillations via Hilfer fractional derivative

Abstract

The present study seeks to understand the forced oscillations through modeling via fractional differential equation, using the derivative according to Hilfer and representing the external force as a succession of delta Dirac functions. This formulation allows recovering the solutions according to Caputo and Riemann-Liouville. The results obtained show that both Caputo and Riemann Liouville solutions coincide when we recover the entire order of the derivative. Also, by switching the order of the derivative it is possible to simulate damping.