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

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  • Raja, Muhammad Asif Zahoor
  • Samar, Raza
  • Manzar, Muhammad Anwar
  • Shah, Syed Muslim

Abstract

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.

Suggested Citation

  • Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
    • Handle: RePEc:eee:matcom:v:132:y:2017:i:c:p:139-158
    DOI: 10.1016/j.matcom.2016.08.002
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    1. Aguilera-Venegas, Gabriel & Galán-García, José L. & Mérida-Casermeiro, Enrique & Rodríguez-Cielos, Pedro, 2014. "An accelerated-time simulation of baggage traffic in an airport terminal," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 58-66.
    2. Aguilera, Gabriel & Galán, José Luis & García, José Manuel & Mérida, Enrique & Rodríguez, Pedro, 2014. "An accelerated-time simulation of car traffic on a motorway using a CAS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 21-30.
    3. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    4. Lo Schiavo, Mauro & Prinari, Barbara & Gronski, Jessica A. & Serio, Angelo V., 2015. "An artificial neural network approach for modeling the ward atmosphere in a medical unit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 116(C), pages 44-58.
    5. Yang, Yongqing & Cao, Jinde & Xu, Xianyun & Hu, Manfeng & Gao, Yun, 2014. "A new neural network for solving quadratic programming problems with equality and inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 103-112.
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    Cited by:

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