FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

• Published in: Computational & applied mathematics Vol. 39; no. 4
• Main Authors: Sabir, Zulqurnain, Raja, Muhammad Asif Zahoor, Shoaib, Muhammad, Aguilar, J. F. Gómez
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2020; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Comparative studies; Computation; Computational mathematics; Computational Mathematics and Numerical Analysis; Evolution; Genetic algorithms; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Neural networks; Optimization; Quadratic programming; Robustness (mathematics); Solvers; Stability analysis; Statistical analysis; Sequential quadratic programming; 34A34; Multi-singular systems; Artificial neural networks; Meyer wavelet neural networks; 82B31; 34-XX; Multi-fractional Lane–Emden model; Genetic algorithms; 34A08
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-020-01350-0

In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane–Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNEICS for DSMF-LES is presented after derivation from standard Lane–Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the mean-squared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.