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

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Najeeb Alam Khan , Amber Shaikh , Muhammad Asif Zahoor Raja , Shafqat Ullah Khan ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1515/jamsi-2016-0009

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.

Related Topics

Mathematics

Simulated Annealing

Differential Equation

Mathematical Analysis

Algorithm

Computer Science

Artificial Intelligence

Wavelet Transform

Discrete Wavelet Transform

Concepts

Legendre polynomials Legendre wavelet Mathematics Taylor series Fuzzy logic Simulated annealing Applied mathematics Residual Associated Legendre polynomials Differential equation Artificial neural network Computational intelligence Mathematical analysis Orthogonal polynomials Gegenbauer polynomials Classical orthogonal polynomials Mathematical optimization Algorithm Computer science Artificial intelligence Wavelet transform Discrete wavelet transform Wavelet

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Type: article
Language: en
Landing Page: https://doi.org/10.1515/jamsi-2016-0009
PDF: https://content.sciendo.com/downloadpdf/journals/jamsi/12/2/article-p67.pdf
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Cited By: 4
References: 35
Related Works: 10
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DOI: https://doi.org/10.1515/jamsi-2016-0009

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

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Language: en

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Publication year: 2016

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Publication date: 2016-12-01

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Authors: Najeeb Alam Khan, Amber Shaikh, Muhammad Asif Zahoor Raja, Shafqat Ullah Khan

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Landing page: https://doi.org/10.1515/jamsi-2016-0009

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Concepts: Legendre polynomials, Legendre wavelet, Mathematics, Taylor series, Fuzzy logic, Simulated annealing, Applied mathematics, Residual, Associated Legendre polynomials, Differential equation, Artificial neural network, Computational intelligence, Mathematical analysis, Orthogonal polynomials, Gegenbauer polynomials, Classical orthogonal polynomials, Mathematical optimization, Algorithm, Computer science, Artificial intelligence, Wavelet transform, Discrete wavelet transform, Wavelet

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Cited by: 4

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Citations by year (recent): 2022: 1, 2020: 1, 2019: 1, 2018: 1

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