This paper is concerned with the numerical solution of initial value problems for a linear differential equation of fractional order (the so-called Bagley-Torvik equation):
where , are real constants and a given real function. Here denotes the fractional differential operator of order in the sense of Canuto [the authors use the definition given by R. Gorenflo and F. Mainardi Fractional calculus: Integral and differential equations of fractional order in A. Carpinteri and F. Mainerdi (ed.), Fractal and Fractional Calculus in Continuum Mechanics: pp. 223–276 (1997; Zbl 0917.73004), Chapter 5].
In the paper under consideration the second order equation is written as an equivalent system of four fractional differential equations of order 1/2 arid then linear multistep methods that approximate the fractional order derivatives and are consistent and stable are proposed. In particular, predictor-corrector methods of Adams-Bashforth-Moulton type are given and some convergence results are established.