<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on fractional fuzzy initial value problem (FFIVP) with triangular condition. Here, Legendre polynomials are used to modify the structure of neural networks with a Taylor series approximation of the tangent hyperbolic as activation function while the network adaptive coefficients are trained in the procedure of simulated annealing to optimize the residual error. The computational results are depicted in terms of numerical values to compare them with previous results.</p></abstract>

In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on fractional fuzzy initial value problem (FFIVP) with triangular condition. Here, Legendre polynomials are used to modify the structure of neural networks with a Taylor series approximation of the tangent hyperbolic as activation function while the network adaptive coefficients are trained in the procedure of simulated annealing to optimize the residual error. The computational results are depicted in terms of numerical values to compare them with previous results.

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Department of Mathematics, University of Karachi, Karachi 75270,

Department of Mathematics, of Karachi, Karachi 75270,

Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock,

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this article, Legendre simulated annealing, neural network (LSANN) is designed for fuzzy fractional order differential equations, which is employed on...

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Published Online: Dec 30, 2016

Page range: 67 - 82

DOI: https://doi.org/10.1515/jamsi-2016-0009

Keywords
Fuzzy, neural network, simulated annealing, Legendre polynomials

© 2016 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Published Online: Dec 30, 2016

Page range: 67 - 82

DOI: https://doi.org/10.1515/jamsi-2016-0009

KeywordsFuzzy, neural network, simulated annealing, Legendre polynomials

© 2016 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Fuzzy, neural network, simulated annealing, Legendre polynomials