Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley-Torvik equation

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• 作者：Muhammad Asif Zahoor Raja^a ; ^{muhammad.asif@ciit-attock.edu.pk" class="auth_mail" title="E-mail the corresponding author} ; ^{asif.phdee10@iiu.edu.pk" class="auth_mail" title="E-mail the corresponding author} ; ^{rasifzahoor@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Raza Samar^b ; ^{rsamar@jinnah.edu.pk" class="auth_mail" title="E-mail the corresponding author} ; Muhammad Anwar Manzar^c ; ^{anwaar.phdee08@iiu.edu.pk" class="auth_mail" title="E-mail the corresponding author} ; Syed Muslim Shah^b ; ^{smshah77@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bagley&ndash ; Torvik equation ; Fractional differential equations ; Interior point algorithm ; Neural networks ; Unsupervised modeling
• 刊名：Mathematics and Computers in Simulation
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：132
• 期：Complete
• 页码：139-158
• 全文大小：2908 K

文摘

In this article, an efficient computing technique has been developed for the solution of fractional order systems governed with initial value problems (IVPs) of the Bagley–Torvik equations using fractional neural networks (FNNs) optimized with interior point algorithms (IPAs). The strength of FNNs is exploited to develop an approximate model of the equation in an unsupervised manner. The training of optimal weight of the networks is carried out using IPAs. The designed scheme is evaluated on different IVPs of the equation. Comparative studies for the results of the proposed scheme are made with an available exact solution, Podlubny numerical techniques, an analytical solver based on He’s variational iteration method and a reported solution of stochastic solvers based on hybrid approaches, in order to verify the correctness of the design scheme. The results of statistical analysis based on the sufficient large number of independent runs established the consistency of the proposed scheme in terms of accuracy and convergence.