A Numerical Method for Delayed Fractional-Order Differential Equations

Abstract EN

A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised.

The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition.

The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations.

Meanwhile, the detailed error analysis for this algorithm is given.

In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method.