A numerical method for solving fractional differential equations by using neural network

DOI10.1155/2015/439526zbMath1378.65156OpenAlexW1945981180WikidataQ59102481 ScholiaQ59102481MaRDI QIDQ277663

Xuan Liu, Hai-Dong Qu

Publication date: 2 May 2016

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2015/439526

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Numerical methods for ordinary differential equations (65L99) Fractional ordinary differential equations (34A08)

Related Items (11)

A Runge–Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives ⋮ Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems ⋮ Solving fractional differential equations of variable-order involving operators with Mittag-Leffler kernel using artificial neural networks ⋮ A highly accurate artificial neural networks scheme for solving higher multi‐order fractal‐fractional differential equations based on generalized Caputo derivative ⋮ A generalized Taylor operational matrix method for ψ‐fractional differential equations ⋮ Numerical solutions of wavelet neural networks for fractional differential equations ⋮ Solving FDE by trigonometric neural network and its applications in simulating fractional HIV model and fractional Schrodinger equation ⋮ Performance of Genocchi wavelet neural networks and least squares support vector regression for solving different kinds of differential equations ⋮ Solving fractional differential equations by using triangle neural network ⋮ Direct and integrated radial functions based quasilinearization schemes for nonlinear fractional differential equations ⋮ A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order

Uses Software

• Khan Academy
• ma2dfc

Cites Work

• Unnamed Item
• Monotone iterative technique for Riemann-Liouville fractional integro-differential equations with advanced arguments
• A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments
• Existence of solutions for fractional impulsive differential equations with \(p\)-Laplacian operator
• Solving the fractional BBM-Burgers equation using the homotopy analysis method
• Homotopy perturbation method for nonlinear partial differential equations of fractional order
• Homotopy analysis method for solving a class of fractional partial differential equations
• A new stochastic approach for solution of Riccati differential equation of fractional order
• A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
• Homotopy analysis method for solving multi-term linear and nonlinear diffusion-wave equations of fractional order
• Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
• Existence results for a class of second order evolution inclusions and its corresponding first order evolution inclusions
• Existence of nonnegative solutions for a fractional \(m\)-point boundary value problem at resonance
• Numerical methods for nonlinear partial differential equations of fractional order
• EXISTENCE AND GLOBAL BIFURCATION OF PERIODIC SOLUTIONS TO A CLASS OF DIFFERENTIAL VARIATIONAL INEQUALITIES
• Fractional kinetic equations: solutions and applications
• Homotopy analysis method for solving fractional hyperbolic partial differential equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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