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Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network
Author(s) -
Hadian Rasanan Amir Hosein,
Bajalan Nastaran,
Parand Kourosh,
Rad Jamal Amani
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5981
Subject(s) - nonlinear system , artificial neural network , mathematics , fractional calculus , fractional programming , partial differential equation , mathematical optimization , computer science , artificial intelligence , mathematical analysis , nonlinear programming , physics , quantum mechanics
By the rapid growth of available data, providing data‐driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive‐decision‐making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg‐Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible.