A fractional study based on the economic and environmental mathematical model

The purpose of this investigation is to provide the numerical study based on the frac-tional order (FO) economic and environmental mathematical model (EEMM) called as FO-EEMM. The motive of this work is to find more realistic results of the EEMM of the non-integer and FO derivatives. The structure of the FO-EEMM is categorized into three dynamics, control accomplishment cost, capability of the manufacturing elements and the diagnostics cost of the technical exclusion. The solution of the FO-EEMM is numerically presented by using the scaled conjugate gradient neural networks (SCGNNs). Three cases based on the FO-EEMM have been scrutinized to indicate the numerical performances along with the selection of the statics as 76% for training, 13% for testing and 11% for certification. The correctness of the designed SCGNNs is authenticated by using the matching of the achieved and the reference solutions (Adams-Bashforth-Moulton). The validity, exactness, dependability, and competence of the SCGNNs is observed through the performances of the mean square error, regression, state transi-tions, error histograms and correlation.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

The purpose of this investigation is to numerically study the fractional order economic and environmental mathematical model (FO-EEMM). The study aims to find more realistic results of the FO-EEMM with non-integer and fractional order derivatives. The FO-EEMM is divided into three aspects: control accomplishment cost, capability of manufacturing elements, and diagnostics cost of technical exclusion. The FO-EEMM's solution is presented numerically using scaled conjugate gradient neural networks (SCGNNs). Three cases based on the FO-EEMM have been examined to evaluate numerical performances.