Theoretical fractional formulation of a three-dimensional radio frequency ion trap (Paul-trap) for optimum mass separation

We investigate the dynamics of an ion confined in a Paul-trap supplied by a fractional periodic impulsional potential. The Cantor-type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian-coordinate systems to Cantor-type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor-type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor-type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul-trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.