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SM ISO690:2012 JAFARIAN, Ahmad, MEASOOMY NIA, Safa. Fractional order integro-differential equations solution by artificial neural networks approach. In: Conference on Applied and Industrial Mathematics: CAIM 2017, 14-17 septembrie 2017, Iași. Chișinău: Casa Editorial-Poligrafică „Bons Offices”, 2017, Ediţia 25, p. 32. ISBN 978-9975-76-247-2. |
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Conference on Applied and Industrial Mathematics Ediţia 25, 2017 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, Romania, 14-17 septembrie 2017 | ||||||
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Pag. 32-32 | ||||||
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Great care must be taken in considering the fact that neural networks moved in the direction of a systematic world such as applied mathematics and engineering sciences. Such certain movement helped shaping fantastic changes in the numerical solution of complicated cases which are overt in natural phenomena. In the present study, a comprehensive optimization mechanism consisting of a reliable three-layered feed-forward neural network is formed to solve a class of fractional order ordinary integro-di erential equations. One point should be kept in mind that the supervised backpropagation type learning algorithm which is based on the gradient descent method, is capable of approximating the mentioned problem on an arbitrary interval to any desired degree of accuracy. Besides, some comparative test problems are given to reveal the exibility and eciency of the proposed method. |
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Cuvinte-cheie Fractional order integro-differential equation, Artificial neural networks approach, Least mean squares cost function, Supervised back-propagation learning algorithm |
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