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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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    8. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.
    9. Jadoon, Ihtesham & Raja, Muhammad Asif Zahoor & Junaid, Muhammad & Ahmed, Ashfaq & Rehman, Ata ur & Shoaib, Muhammad, 2021. "Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu’s oscillatory systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 444-470.

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