A fractional order dynamical trajectory approach for optimization problem with HPM

Abstract

In this paper, the homotopy perturbation method (HPM) is applied to solve nonlinear programming (NLP) problem on the basis of the fractional order differential equations system. The trajectory of the proposed fractional order dynamical system is approached to the optimal solution for optimization problem. The multistage strategy is used to show this behavior of the system trajectory in large timespan. The ability of the method to obtain approximate analytical solutions was shown by comparisons among the multistage HPM, the standard HPM and the fourth order Runge-Kutta method.