@Article{cmc.2023.032950,
AUTHOR = {Wajaree Weera, Chantapish Zamart, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Afaf S. Alwabli, S. R. Mahmoud, Supreecha Wongaree, Thongchai Botmart},
TITLE = {Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {74},
YEAR = {2023},
NUMBER = {1},
PAGES = {1735--1748},
URL = {http://www.techscience.com/cmc/v74n1/49885},
ISSN = {1546-2226},
ABSTRACT = {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.},
DOI = {10.32604/cmc.2023.032950}
}