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Artificial neural network approach for a class of fractional ordinary differential equation

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Date

2017

Authors

Jafarian, Ahmad
Mokhtarpour, Masoumeh
Baleanu, Dumitru

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Springer

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Abstract

The essential characteristic of artificial neural networks which against the logistic traditional systems is a data-based approach and has led a number of higher education scholars to investigate its efficacy, during the past few decades. The aim of this paper was concerned with the application of neural networks to approximate series solutions of a class of initial value ordinary differential equations of fractional orders, over a bounded domain. The proposed technique uses a suitable truncated power series of the solution function and transforms the original differential equation in a minimization problem. Then, the minimization problem is solved using an accurate neural network model to compute the parameters with high accuracy. Numerical results are given to validate the iterative method.

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Feed-Forward Neural Network, Fractional Differential Equation, Approximate Solution, Backpropagation Learning Algorithm

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Citation

Jafarian, Ahma; Mokhtarpour, Masoumeh; Baleanu, Dumitru, "Artificial neural network approach for a class of fractional ordinary differential equation", Neural Computing&Applications, Vol.28, No.4, pp.765-773, (2017).

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Source

Neural Computing&Applications

Volume

28

Issue

4

Start Page

765

End Page

773