Authors: Ahmad Jafarian; Layla Kulaii
Addresses: Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran ' Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran
Abstract: Indeed, the special advantages of artificial neural networks in modelling and solving complex real-world phenomena, have made them powerful computational and mathematical tools in applied sciences and engineering. The main purpose of this paper is to derive an iterative method based on a combination of neural nets approach and power-series method for an approximate treatment of the fractional Bratu-type equations. Supposedly, the problem considered has a solution in terms of the series expansion of unknown function, the proper implementation of a suitable neural architecture leads to estimate the unknown series coefficients, systematically. So as to show practical applicability and robustness of this technique, Bratu's boundary value problem in one-dimensional planar is solved as numerical example. Achieved numerical and simulative results reveal that the method is very effective and powerful.
Keywords: artificial neural network; back-propagation learning algorithm; criterion function; fractional Bratu-type; power-series polynomial; problem.
International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.2, pp.142 - 156
Received: 15 Jan 2016
Accepted: 04 Aug 2016
Published online: 01 Aug 2017 *