Solving fractional differential equations of variable-order involving operators with Mittag-Leffler kernel using artificial neural networks
| Autor: | Ricardo Fabricio Escobar-Jiménez, H. M. Romero-Ugalde, C. J. Zúñiga-Aguilar, Martin Valtierra-Rodriguez, José Francisco Gómez-Aguilar |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Artificial neural network
General Mathematics Applied Mathematics Computer Science::Neural and Evolutionary Computation Mathematical analysis General Physics and Astronomy Order (ring theory) Statistical and Nonlinear Physics 02 engineering and technology 01 natural sciences 010305 fluids & plasmas Fractional calculus Fractional programming Kernel (statistics) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0103 physical sciences 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Fractional differential Approximate solution Mathematics Variable (mathematics) |
| Zdroj: | Chaos, Solitons & Fractals. 103:382-403 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2017.06.030 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect