2025/02/22 by Farahnaz Golpour Lasaki, Golpour Lasaki, Farahnaz, Hamideh Ebrahimi +3
Engineering · Mathematics · #Advanced Control Systems Design #Fractional Differential Equations Solutions #Functional link neural network #Lagrange polynomials #Numerical methods for differential equations #Time-varying delay #Variable-order fractional operators
paper · doi:10.82521/ijo.2024.120026
openalex publication_date 2025/02/22 · openalex created_date 2025/12/27 · openalex updated_date 2026/07/07
This paper presents a novel functional link neural network for solving a class of variable-order fractional partial differential equations with time-varying delay. Due to the proficiency of Lagrange polynomials in numerical approximations for fractional calculus, these polynomials serve as the foundational neuro-solutions within the neural network. Finding the right activation functions is essential for effective learning in artificial neural networks, particularly when solving variable-order fractional derivatives and time-varying delays. To reduce the computational complexity of the proposed neural network, a linear activation function is used. Numerical simulations are carried out to demonstrate the capability of the proposed method. The neural network undergoes training using a modified Newton-Raphson method instead of the traditional learning techniques. The study’s findings indicate that the suggested functional link neural network achieves greater accuracy in comparison to some traditional methods for solving fractional partial differential equations.