Equations of Motion for Ideal Hydrodynamics in Rotating Frame Using Caputo's Definition

Abstract

In this paper, we describe the motion of ideal hydrodynamics in a rotating frame by the equations of motion using Caputo's fractional derivative. Then, from the fractional Euler-Lagrangian equation, we obtain the equations that describe the motion of ideal fluid in fractional form, the Hamiltonian density and the energy-stress tensor obtained in fractional form from the fluid Lagrangian density. Finally, from the Hamiltonian density, we also find the Hamiltonian equations of motion for the ideal fluid in fractional form.

Keywords: Ideal fluid Lagrangian density, Caputo’s definition, Fractional Hamiltonian.