Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model

Abstract

The aim of this study is to design a singular fractional order pantograph differential model by using the typical form of the Lane-Emden model. The necessary details of the singular-point, fractional order and shape factor of the designed model are also provided. The numerical solutions of the designed model have been presented using the combination of the fractional Meyer wavelet (FMW) neural networks (NNs) modeling and optimization of global search with genetic algorithm (GA) supported with local search of sequential quadratic programming (SQP), i.e., FMWNN-GASQP. The strength of FMWNN is employed to design an objective function using the differential model along with its initial conditions of the singular fractional order pantograph model. The optimization of this objective function is performed using the integrated competence of GA-SQP. The verification, perfection and authentication of the singular fractional order pantograph model using fractional Meyer computing solver is observed for different cases through comparative studies from the available exact solutions which endorsed its robustness, convergence and stability. Moreover, the statistics observation with necessary explanations further authenticate the performance of the FMWNN-GASQP in terms of accuracy and reliability.