The primary goal of this work is the implementation of a new linear integral operator to fully account for finite Larmor radius effects from the plasma particle gyration. Compared to the existing approach based on a Larmor radius expansion of the plasma conductivity operator, this development will allow for a more accurate description of the plasma response in cases where the width of the resonant current, which shields the perturbations, becomes comparable with the ion Larmor radius. In particular, possible coupling to artificial short- scale solutions ("fake modes") sometimes present for plasma conductivity operators based on Larmor radius expansions should be avoided for an integral operator. In addition, extended computations for full toroidal plasma geometry by hybrid kinetic-magnetohydrodynamic modeling shall be performed. The work is performed in the context of a dissertation.