Numerical solution of fractional-order time-varying delayed differential systems using Lagrange interpolation

In this paper, a numerical solution of fractional-order time-varying delayed differential systems using Lagrange interpolation is investigated. Based on Lagrange interpolation method, the Adams–Bashforth–Moulton algorithm has been extended to solve fractional-order time-varying delayed differential systems. Furthermore, a detailed error analysis of this algorithm is presented. A fractional-order time-varying delayed Hopfield neural network as numerical example is given. In addition, the different parameters in the fractional-order time-varying delayed neural network are considered. Finally, some simple and direct numerical methods which are compared with Lagrange interpolation method in the fractional-order time-varying delayed neural network are discussed. The example with numerical simulation clearly illustrated that the present method is reliable.