Solving differential equations of fractional order using an optimization technique based on training artificial neural network

M. Pakdaman, A. Ahmadian, S. Effati, S. Salahshour and D. Baleanu

Applied Mathematics and Computation, 2017, vol. 293, issue C, 81-95

Abstract: The current study aims to approximate the solution of fractional differential equations (FDEs) by using the fundamental properties of artificial neural networks (ANNs) for function approximation. In the first step, we derive an approximate solution of fractional differential equation (FDE) by using ANNs. In the second step, an optimization approach is exploited to adjust the weights of ANNs such that the approximated solution satisfies the FDE. Different types of FDEs including linear and nonlinear terms are solved to illustrate the ability of the method. In addition, the present scheme is compared with the analytical solution and a number of existing numerical techniques to show the efficiency of ANNs with high accuracy, fast convergence and low use of memory for solving the FDEs.

Keywords: Multi-term fractional differential; equations; Artificial neural network; Optimization; Caputo derivative (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:293:y:2017:i:c:p:81-95

DOI: 10.1016/j.amc.2016.07.021

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