deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations

Avatar
Poster
Voices Powered byElevenlabs logo
Connected to paper

deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations

Authors

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

Abstract

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the proposed design. In each equation, a deep neural network is used to approximate the unknown function. Three forms of fractional differential equations have been examined to highlight the method's versatility: a fractional ordinary differential equation, a fractional order integrodifferential equation, and a fractional order partial differential equation. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.

Follow Us on

0 comments

Add comment