Homotopy perturbation aided optimization procedure with applications to oscillatory fractional order nonlinear dynamical systems

Abstract

This paper presents an approximate solution of nonlinear fractional differential equations (FDEs) that exhibit an oscillatory behavior by using a metaheuristic technique. The solutions of the governing equations are approximated by using homotopy perturbation method (HPM) along with the fractional derivative in the Caputo sense. The designed methodology is based on a weighted series of HPM in conjunction with a nature-inspired algorithm. The idea is instantly fascinated by the researchers on the consequent implementation of nature-inspired learning algorithms such as a Cuckoo search algorithm (CSA). The usage of CSA has accelerated the minimized search path of error to the convergent values of the solution. The validity and accuracy of the proposed technique are ascertained by calculating the approximate solution and the error norms which ensure the convergence of the approximation that can be further increased. The critical analysis is also provided by the numerical simulation of two different test models. Discussion of key points has been determined by the tabulation of numerical values and graphs. Comparative study of the results with known numerical technique is also performed.