Institute of Cosmophysical Research and Radio Wave Propagation

Application of a Neural-Network Algorithm Based on Orthogonal Laguerre Polynomials to the Solution of the Cauchy Problem for Differential Equations with a Variable-Order Fractional Derivative on the Example of the Fractional Lane–Emden Equation

This paper proposes, implements, and tests a neural-network method based on orthogonal Laguerre polynomials for the numerical solution of the Cauchy problem for a singular nonlinear Lane–Emden equation with a variable-order fractional derivative. Such equations rarely admit analy...