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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