Application of the Adams-Bashfort-Mowlton Method to the Numerical Study of Linear Fractional Oscillators Models

The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) method is considered a numerical analysis tool. An analysis of the errors of the methods is carried out, and it is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method.