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.

在这项研究中，针对非线性奇异分数车道-埃姆登（NS-FLE）微分方程，设计了一种基于分数Meyer小波人工神经网络（FMW-ANN）的新型随机计算框架。利用FMW-ANN的建模强度将微分NS-FLE系统转换为差分方程，并在均方误差意义上实现近似理论，以开发NS-FLE微分方程的优值函数。通过利用遗传算法（GA）的全局搜索功效以及有效的活动集（AS）算法对局部细化的支持，混合计算的元启发式强度可用于优化设计变量FMW-ANN，即FMW-ANN-GASA 。拟议的FMW-ANN-GASA方法论是在NS-FLM上针对六种不同情况实施的，目的是检查准确性，收敛性，稳定性和鲁棒性。将拟议的FMW-ANN-GASA数值结果与精确解进行比较，以验证正确性，可行性和有效性。统计观察结果进一步验证了FMW-ANN-GASA对于奇异非线性分数阶系统解的价值。