New combinative method for solving one-dimensional fractional Bratu differential equation Online publication date: Tue, 15-Aug-2017
by Ahmad Jafarian; Layla Kulaii
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 7, No. 2, 2017
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.
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