Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model

The aim of this research is to present an investigation based on the fractional derivatives and perturbation factors for the novel singular system. This study also presents a novel design of the fractional perturbed singular system by using the conventional Lane-Emden form together with the features of fractional order values, singular points, perturbed terms and shape factors. An analysis based on the fractional order derivative and perturbation factors is provided using the novel singular form of the Lane-Emden system in two different ways with three different variations. The numerical representations based on the novel design of the fractional perturbed singular system are presented through the Meyer wavelet neural networks (MWNNs). The optimization is performed by using the hybrid efficiency of the global swarming particle swarm optimization (PSO) scheme along with the local interior-point algorithm (IPA). The modeling through the MWNN is signified through the novel fractional perturbed singular system through the mean square error along with the PSOIPA optimization. The exactness, verification, endorsement and excellence of the novel fractional perturbed singular system are authenticated through the comparison of the obtained and the true solutions. The reliability of the stochastic procedure is performed by using the statistical measures with a large domain of the dataset to analyze the fractional derivatives and perturbation factors for the novel singular system.