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.
| Published in | Applied and Computational Mathematics (Volume 2, Issue 6) |
| DOI | 10.11648/j.acm.20130206.19 |
| Page(s) | 159-162 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Fractional Differential Equations, Cosine Basis Neural Network Algorithm, Initial Value Problem
| [1] | R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: afractional dynamics approach, Phys. Rep. 339 (1) (2000) 1-77. |
| [2] | I. Podlubny, et al. Matrix approach to discrete fractional calculus II: Partial fractional differential equations, Journal of Computational Physics. 228(2009) 3137-3153. |
| [3] | H.D. Qu, X. Liu. Existence of nonnegative solutions for fractional m-point boundary value problem at resonance. Boundary Value Problems 2013, 2013:127. doi: 10.1186/1687-2770-2013-127 |
| [4] | A. Elsaid. Homotopy analysis method for solving a class of fractional partial differential equations, Commun. Nonlinear Sci. Numer Simulat. 16 (2011)3655-3664. |
| [5] | A.A.Kilbsa, H.M.Srivastava, J.J.Trujillo. Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. |
APA Style
Luo Xiaodan, Junmin Zhang. (2013). Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Applied and Computational Mathematics, 2(6), 159-162. https://doi.org/10.11648/j.acm.20130206.19
ACS Style
Luo Xiaodan; Junmin Zhang. Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Appl. Comput. Math. 2013, 2(6), 159-162. doi: 10.11648/j.acm.20130206.19
AMA Style
Luo Xiaodan, Junmin Zhang. Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Appl Comput Math. 2013;2(6):159-162. doi: 10.11648/j.acm.20130206.19
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20130206.19,
author = {Luo Xiaodan and Junmin Zhang},
title = {Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations},
journal = {Applied and Computational Mathematics},
volume = {2},
number = {6},
pages = {159-162},
doi = {10.11648/j.acm.20130206.19},
url = {https://doi.org/10.11648/j.acm.20130206.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.19},
abstract = {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.},
year = {2013}
}
TY - JOUR T1 - Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations AU - Luo Xiaodan AU - Junmin Zhang Y1 - 2013/01/10 PY - 2013 N1 - https://doi.org/10.11648/j.acm.20130206.19 DO - 10.11648/j.acm.20130206.19 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 159 EP - 162 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20130206.19 AB - 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. VL - 2 IS - 6 ER -
Information
Email: