On artificial neural networks approach with new cost functions

Jafarian A., Measoomy Nia S., Khalili Golmankhaneh A., Baleanu D.

Applied Mathematics and Computation, vol.339, pp.546-555, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 339
  • Publication Date: 2018
  • Doi Number: 10.1016/j.amc.2018.07.053
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.546-555
  • Keywords: Artificial neural networks approach, Fractional order ordinary differential equation, Least mean squares cost function, Supervised back-propagation learning algorithm
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this manuscript, the artificial neural networks approach involving generalized sigmoid function as a cost function, and three-layered feed-forward architecture is considered as an iterative scheme for solving linear fractional order ordinary differential equations. The supervised back-propagation type learning algorithm based on the gradient descent method, is able to approximate this a problem on a given arbitrary interval to any desired degree of accuracy. To be more precise, some test problems are also given with the comparison to the simulation and numerical results given by another usual method.