Tide level changes as fractional dynamics: A generalized harmonic oscillator

A new concept of fractional dynamics in the equation of motion, that is, a generalized harmonic oscillator (GHO) in non-Euclidean space, is applied to analyze tidal fluctuations observed at Katsuura and Yamaguchi, Japan, and Dili Port, East Timor (near the equator), as a case example. The frequency spectrum (FS) in the frequency domain is shown to be replicated well by the GHO. It is also shown that the FS extracted from underwater acoustic noises, well established in recent atmospheric environmental fields, is in accord with those found in actual tidal changes, even at different locations and times, suggesting that both effects can be dominated by fractional dynamics.