Solving fractional differential equations by using triangle neural network
type: Item
instance of: scholarly article
title: Solving fractional differential equations by using triangle neural network
zbMATH Open document ID: 1469.65119
DOI: 10.1155/2021/5589905
author: Yanyan Li
published in: Journal of Function Spaces
publication date: 2021-05-17T00:00:00Z
review text: Summary: In this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The fractional derivative is considered Caputo type. The fractional derivative of the triangle neural network is analyzed first. Then, based on the technique of minimizing the loss function of the neural network, the proposed numerical methods reduce the fractional differential equation into a gradient descent problem or the quadratic optimization problem. By using the gradient descent process or the quadratic optimization process, the numerical solution to the FDEs can be obtained. The efficiency and accuracy of the presented methods are shown by some numerical examples. Numerical tests show that this approach is easy to implement and accurate when applied to many types of FDEs.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 68T07
zbMATH DE Number: 7348532
zbMATH Keywords: fractional differential equations
zbMATH Keywords: artificial neural networks
zbMATH Keywords: quadratic optimization
Wikidata QID: Q115243684
describes a project that uses: ma2dfc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5589905
OpenAlex ID: W3156662254
cites work: Q3141902
cites work: Q3864730
cites work: Q5699297
cites work: Q4233638
cites work: What is a fractional derivative?
cites work: Numerical methods for nonlinear partial differential equations of fractional order
cites work: Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
cites work: A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments
cites work: Monotone iterative technique for nonlinear boundary value problems of fractional order \(p\in(2,3]\)
cites work: Existence and global bifurcation of periodic solutions to a class of differential variational inequalities
cites work: Existence of nonnegative solutions for a fractional \(m\)-point boundary value problem at resonance
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
cites work: A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
cites work: Homotopy analysis method for solving fractional hyperbolic partial differential equations
cites work: Homotopy analysis method for solving a class of fractional partial differential equations
cites work: Artificial Neural Network Approximation of Fractional-Order Derivative Operators: Analysis and DSP Implementation
cites work: Approximation solution of fractional partial differential equations by neural networks
cites work: A numerical method for solving fractional differential equations by using neural network
description: scientific article; zbMATH DE number 7348532