A Novel Neural Network Architecture for Solving Fractional Differential Equations

Dana Mazraeh, Hassan; Nosrati Firoozsalari, Ali; Afzal Aghaei, Alireza; Parand, Kourosh

doi:10.22034/cmde.2025.63059.2803

A Novel Neural Network Architecture for Solving Fractional Differential Equations

Articles in Press

Document Type : Research Paper

Authors

¹ School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.

² Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

10.22034/cmde.2025.63059.2803

Abstract

The primary objective of this research is to develop a neural network-based method for solving fractional differential equations. The proposed design incorporates a Gaussian integration rule and an $L1$ discretization technique for solving fractional (integro-) differential equations. In each equation, a multi-layer neural network is employed to approximate the unknown function. To demonstrate the versatility of the method, three forms of fractional differential equations are examined: a fractional ordinary differential equation, a fractional integro-differential equation, and a fractional partial differential equation. The results indicate that the proposed architecture demonstrates good accuracy for these different types of equations.

Keywords

Main Subjects