TY - EJOU
AU - Weera, Wajaree
AU - Zamart, Chantapish
AU - Sabir, Zulqurnain
AU - Raja, Muhammad Asif Zahoor
AU - Alwabli, Afaf S.
AU - Mahmoud, S. R.
AU - Wongaree, Supreecha
AU - Botmart, Thongchai
TI - Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network
T2 - Computers, Materials \& Continua
PY - 2023
VL - 74
IS - 1
SN - 1546-2226
AB - The motive of these investigations is to provide the importance and significance of the fractional order (FO) derivatives in the nonlinear environmental and economic (NEE) model, i.e., FO-NEE model. The dynamics of the NEE model achieves more precise by using the form of the FO derivative. The investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this study. The composition of the FO-NEE model is classified into three classes, execution cost of control, system competence of industrial elements and a new diagnostics technical exclusion cost. The mathematical FO-NEE system is numerically studied by using the artificial neural networks (ANNs) along with the Levenberg-Marquardt backpropagation method (ANNs-LMBM). Three different cases using the FO derivative have been examined to present the numerical performances of the FO-NEE model. The data is selected to solve the mathematical FO-NEE system is executed as 70% for training and 15% for both testing and certification. The exactness of the proposed ANNs-LMBM is observed through the comparison of the obtained and the Adams-Bashforth-Moulton database results. To ratify the aptitude, validity, constancy, exactness, and competence of the ANNs-LMBM, the numerical replications using the state transitions, regression, correlation, error histograms and mean square error are also described.
KW - Environmental and economic model; artificial neural networks; fractional order; nonlinear; Levenberg-Marquardt backpropagation
DO - 10.32604/cmc.2023.032950