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

• URL: http://arxiv.org/abs/2309.07684v1
• Date: Thu, 14 Sep 2023 12:58:40 GMT
• Title: deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations
• Authors: Ali Nosrati Firoozsalari, Hassan Dana Mazraeh, Alireza Afzal Aghaei, and Kourosh Parand
• Abstract summary: In each fractional differential equation, a deep neural network is used to approximate the unknown function. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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