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Neural Computing and Applications

, Volume 31, Supplement 1, pp 359–378 | Cite as

Fractional neural network models for nonlinear Riccati systems

  • Sadia Lodhi
  • Muhammad Anwaar Manzar
  • Muhammad Asif Zahoor RajaEmail author
Original Article

Abstract

In this article, strength of fractional neural networks (FrNNs) is exploited to find the approximate solutions of nonlinear systems based on Riccati equations of arbitrary order. The feed-forward artificial FrNN are used to develop the energy function of the system by defining an error function in mean square sense. Design parameters for optimization of the energy function are adapted using viable local search with interior point methods (IPMs). The performance of design methodology in terms of accuracy and convergence is analyzed for two different variants of the nonlinear system. Comparison of the results with the exact solutions, as well as approximate numerical results, illustrates the correctness of the methodology. The worth of the scheme is established through statistical inferences based on a large number of simulation runs.

Keywords

Fractional neural networks Adams method Fractional differential equation Interior point methods Riccati system 

Notes

Compliance with ethical standards

All the authors of the manuscript declared that there is no research involving human participants and/or animal and material that required informed consent.

Conflict of interest

The authors declare that they have no conflict of interest.

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© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of MathematicsCapital University of Science and TechnologyIslamabadPakistan
  2. 2.Hamdard Institute of Engineering and TechnologyHamdard UniversityIslamabadPakistan
  3. 3.Department of Electrical EngineeringCOMSATS Institute of Information TechnologyAttockPakistan

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