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Entropy 2013, 15(10), 4188-4198; doi:10.3390/e15104188
Article

The Fractional Differential Polynomial Neural Network for Approximation of Functions

Received: 26 August 2013; in revised form: 5 September 2013 / Accepted: 24 September 2013 / Published: 30 September 2013
(This article belongs to the Special Issue Dynamical Systems)
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Abstract: In this work, we introduce a generalization of the differential polynomial neural network utilizing fractional calculus. Fractional calculus is taken in the sense of the Caputo differential operator. It approximates a multi-parametric function with particular polynomials characterizing its functional output as a generalization of input patterns. This method can be employed on data to describe modelling of complex systems. Furthermore, the total information is calculated by using the fractional Poisson process.
Keywords: fractional calculus; fractional differential equations; fractional polynomial neural network fractional calculus; fractional differential equations; fractional polynomial neural network
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Ibrahim, R.W. The Fractional Differential Polynomial Neural Network for Approximation of Functions. Entropy 2013, 15, 4188-4198.

AMA Style

Ibrahim RW. The Fractional Differential Polynomial Neural Network for Approximation of Functions. Entropy. 2013; 15(10):4188-4198.

Chicago/Turabian Style

Ibrahim, Rabha W. 2013. "The Fractional Differential Polynomial Neural Network for Approximation of Functions." Entropy 15, no. 10: 4188-4198.


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