Open Access

ARTICLE

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

by Prem Junswang¹, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Waleed Adel^4,5, Thongchai Botmart^6,*, Wajaree Weera⁶

1 Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
3 Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan
4 Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Egypt
5 Université Française D’Egypte, Ismailia Desert Road, El-Shorouk, Cairo, Egypt
6 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

* Corresponding Author: Thongchai Botmart. Email:

Computers, Materials & Continua 2022, 72(3), 5015-5030. https://doi.org/10.32604/cmc.2022.027523

Received 19 January 2022; Accepted 16 March 2022; Issue published 21 April 2022

Abstract

The purpose of this paper is to present a numerical approach based on the artificial neural networks (ANNs) for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system. The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation (LMB), named the ANNs-LMB. This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution. Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model. The selection of the data to solve the fractional-order chaotic financial model are selected as 75% for training, 10% for testing, and 15% for certification. The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise. The obtained results are testified to reduce the mean square error (MSE) for solving the fractional model and verified through the various measures including correlation, MSE, regression histogram of the errors, and state transition (ST).

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Keywords

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