Title: New combinative method for solving one-dimensional fractional Bratu differential equation

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.

DOI: 10.1504/IJDSDE.2017.085827

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: 15 Aug 2017 *

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