Analysis of perturbation factors and fractional order derivatives for the novel singular model using the fractional Meyer wavelet neural networks

Abstract

In this study, an analysis of the perturbation factors and fractional order derivatives is performed for the novel singular model. The design of the perturbed fractional order singular model is presented by using the traditional form of the Lane-Emden along with the detail of singular points, fractional order, shape, and perturbed factors. The analysis of the perturbation factors and fractional order terms for the singular model is provided in two steps by taking three different values of the perturbed term as well as fractional order derivatives. The numerical analysis of the perturbation and fractional order terms for the novel fractional Meyer wavelet neural network (FMWNN) along with the global and local search effectiveness of the genetic algorithm (GA) and active-set algorithm (ASA) called as FMWNN-GAASA. The modeling of the FMWNN is presented in terms of mean square error, while the optimization is performed through the GAASA. The authentication, validation, excellence, and correctness of the singular model are observed by using the comparative performances of the obtained and the reference solutions. The stability of the proposed stochastic scheme is observed through the statistical performances for taking large datasets to present the analysis of the perturbation and fractional order terms.