Journal
CHAOS SOLITONS & FRACTALS
Volume 103, Issue -, Pages 382-403Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2017.06.030
Keywords
Fractional calculus; Nonlinear fractional differential equations; Atangana-Baleanu-Caputo fractional derivative; Variable-order fractional derivative; Artificial neural networks
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Funding
- CONACyT
- CONACyT: Catedras CONACyT para jovenes investigadores
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In this paper, we approximate the solution of fractional differential equations using a new approach of artificial neural network. We consider fractional differential equations of variable-order with Mittag-Leffler kernel in Liouville-Caputo sense. With this new neural network approach, it is obtained an approximate solution of the fractional differential equation and this solution is optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional differential equations, the Willamowski-Rossler oscillator and a multi-scroll system. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network different performance indices were calculated. (C) 2017 Elsevier Ltd. All rights reserved.
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