Fractional Mayer Neuro-Swarm Heuristic Solver for Multi-Fractional Order Doubly Singular Model Based on Lane-Emden Equation

Abstract

This research is related to present a novel fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane-Emden (LE) equation using combined investigations of the Mayer wavelet (MW) neural networks (NNs) optimized by the global search effectiveness of particle swarm optimization (PSO) and interior-point (IP) method, i.e. MW-NN-PSOIP. The design of novel fractional Mayer neuro-swarming intelligent solver for multi-fractional order doubly singular LE equation is derived from the standard LE model and the shape factors; fractional order terms along with singular points are examined. The modeling based on the MW-NN strength is implemented to signify the multi-fractional order doubly singular LE model using the ability of mean squared error in terms of the merit function and the networks are optimized with the integrated capability of PSOIP scheme. The perfection, verification and validation of the fractional Mayer neuro-swarming intelligent solver for three different cases of the multi-fractional order doubly singular LE equation are recognized through comparative investigations from the reference results on different measures based on the convergence, robustness, stability and accuracy. Furthermore, the statics interpretations further validate the performance of the proposed fractional Mayer neuro-swarming intelligent solvers.