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

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 u...

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Veröffentlicht in:arXiv.org 2023-09
Hauptverfasser: Ali Nosrati Firoozsalari, Hassan, Dana Mazraeh, Alireza Afzal Aghaei, Parand, Kourosh
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Sprache:eng
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Zusammenfassung: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.
ISSN:2331-8422