Wajaree Weera¹, Thongchai Botmart^1,*, Charuwat Chantawat¹, Zulqurnain Sabir^2,3, Waleed Adel^4,5, Muhammad Asif Zahoor Raja⁶, Muhammad Kristiawan⁷

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 2711-2724, 2023, DOI:10.32604/cmc.2023.033233

Abstract The main purpose of the study is to present a numerical approach to investigate the numerical performances of the fractional 4-D chaotic financial system using a stochastic procedure. The stochastic procedures mainly depend on the combination of the artificial neural network (ANNs) along with the Levenberg-Marquardt Backpropagation (LMB) i.e., ANNs-LMB technique. The fractional-order term is defined in the Caputo sense and three cases are solved using the proposed technique for different values of the fractional order α. The values of the fractional order derivatives to solve the fractional 4-D chaotic financial system are used between 0 and 1. The data… More >

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

CMC-Computers, Materials & Continua, Vol.72, No.3, pp. 5015-5030, 2022, DOI:10.32604/cmc.2022.027523

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… More >

Zulqurnain Sabir¹, Manoj Gupta², Muhammad Asif Zahoor Raja³, N. Seshagiri Rao⁴, Muhammad Mubashar Hussain⁵, Faisal Alanazi⁶, Orawit Thinnukool⁷, Pattaraporn Khuwuthyakorn^7,*

CMC-Computers, Materials & Continua, Vol.72, No.1, pp. 1627-1644, 2022, DOI:10.32604/cmc.2022.021462

Abstract The purpose of the current investigations is to solve the nonlinear dynamics based on the nervous stomach model (NSM) using the supervised neural networks (SNNs) along with the novel features of Levenberg-Marquardt backpropagation technique (LMBT), i.e., SNNs-LMBT. The SNNs-LMBT is implemented with three different types of sample data, authentication, testing and training. The ratios for these statistics to solve three different variants of the nonlinear dynamics of the NSM are designated 75% for training, 15% for validation and 10% for testing, respectively. For the numerical measures of the nonlinear dynamics of the NSM, the Runge-Kutta scheme is implemented to form… More >