Approximation properties of residual neural networks for fractional differential equations (Q6177827)

scientific article; zbMATH DE number 7733068

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English	Approximation properties of residual neural networks for fractional differential equations	scientific article; zbMATH DE number 7733068

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instance of

scholarly article

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title

Approximation properties of residual neural networks for fractional differential equations (English)

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Communications in Nonlinear Science and Numerical Simulation

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publication date

31 August 2023

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zbMATH Keywords

fractional differential equations

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residual networks

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variational iteration method

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approximate solutions

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.cnsns.2023.107399

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cites work

Advances in Fractional Calculus

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Numerical algorithm based on Adomian decomposition for fractional differential equations

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Numerical solution of fractional integro-differential equations by a hybrid collocation method

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Restricted fractional differential transform for solving irrational order fractional differential equations

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Variational iteration method -- a kind of non-linear analytical technique: Some examples

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Variational iteration method for solving multispecies Lotka-Volterra equations

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A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

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A modified variational iteration method for solving Riccati differential equations

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Numerical and theoretical treatment for solving linear and nonlinear delay differential equations using variational iteration method

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Variational iteration method for solving Fokker-Planck equation

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Variational iterative method: an appropriate numerical scheme for solving system of linear Volterra fuzzy integro-differential equations

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The variational iteration method for solving Riesz fractional partial differential equations

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Variational iteration method for the Burgers' flow with fractional derivatives -- new Lagrange multipliers

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Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients

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An iterative approach for solving fractional optimal control problems

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Fractional variational iteration method and its application

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The fractional variational iteration method using He's polynomials

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A numeric-analytic method for time-fractional Swift-Hohenberg (S-H) equation with modified Riemann-Liouville derivative

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ON THE APPROXIMATE SOLUTIONS FOR A SYSTEM OF COUPLED KORTEWEG–DE VRIES EQUATIONS WITH LOCAL FRACTIONAL DERIVATIVE

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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A deep domain decomposition method based on Fourier features

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Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

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Approximation properties of residual neural networks for Kolmogorov PDEs

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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Uniform error estimates for artificial neural network approximations for heat equations

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EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY

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Q5699297

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Fractional Calculus with Applications in Mechanics

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Application of numerical inverse Laplace transform algorithms in fractional calculus

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Q5558293

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FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

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Identifiers

zbMATH Open document ID

1523.34009

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DOI

10.1016/j.cnsns.2023.107399

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6177827