Neural network method for numerical solution of initial value problems of fractional differential equations

@article{Xiaodan2013NeuralNM,
  title={Neural network method for numerical solution of initial value problems of fractional differential equations},
  author={L{\"U} Xiaodan and Junmin Zhang},
  journal={Applied and Computational Mathematics},
  year={2013},
  volume={2},
  pages={159}
}
In this paper, the cosine basis neural network algorithm is introduced for the initial value problem of fractional differential equations. By training the neural network algorithm, we get the numerical solution of the initial value problem of fractional differential equations successfully. 

Figures from this paper

References

SHOWING 1-8 OF 8 REFERENCES
Homotopy analysis method for solving a class of fractional partial differential equations
Abstract In this paper, the homotopy analysis method is applied to obtain the solution of fractional partial differential equations with spatial and temporal fractional derivatives in Riesz andExpand
Theory and Applications of Fractional Differential Equations
1. Preliminaries. 2. Fractional Integrals and Fractional Derivatives. 3. Ordinary Fractional Differential Equations. Existence and Uniqueness Theorems. 4. Methods for Explicitly solving FractionalExpand
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented andExpand
Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance
AbstractWe consider the fractional differential equation D0+qu(t)=f(t,u(t)),0<t<1, satisfying the boundary conditions Expand
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Abstract Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systemsExpand
Existence of nonnegative solutions for fractional m-point boundary value problem at resonance. Boundary Value Problems
  • 2013
Homotopy analysis method for solving a class of fractional partial differential equations, Commun
  • Nonlinear Sci. Numer Simulat
  • 2011
The random walks guide to anomalous diffusion: afractional dynamics approach
  • Phys. Rep
  • 2000