Journal
ALEXANDRIA ENGINEERING JOURNAL
Volume 60, Issue 2, Pages 2641-2659Publisher
ELSEVIER
DOI: 10.1016/j.aej.2021.01.004
Keywords
Meyer wavelet kernels; Neural networks; Hybrid computing techniques; Lane-Emden equation; Singular systems; Stochastic computing
Categories
Funding
- Ministerio de Ciencia, Innovacion y Universidades [PGC2018-097198-BI00]
- Fundacion Seneca de la Region de Murcia [20783/PI/18]
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The novel FMW-ANN-GASA method integrates the modeling strength of FMW-ANN with the global search efficacy of GA to solve NS-FLE differential equations, demonstrating accuracy and efficacy.
In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN is used to transformed the differential NS-FLE system to difference equations and approximate theory is implemented in mean squared error sense to develop a merit function for NS-FLE differential equations. Meta-heuristic strength of hybrid computing by exploiting global search efficacy of genetic algorithms (GA) supported with local refinements with efficient active-set (AS) algorithm is used for optimization of design variables FMW-ANN., i.e., FMW-ANN-GASA. The proposed FMW-ANN-GASA methodology is implemented on NS-FLM for six different scenarios in order to exam the accuracy, convergence, stability and robustness. The proposed numerical results of FMW-ANN-GASA are compared with exact solutions to verify the correctness, viability and efficacy. The statistical observations further validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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