A fractional study based on the economic and environmental mathematical model

Abstract

The purpose of this investigation is to provide the numerical study based on the fractional 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 transitions, error histograms and correlation.

Keywords

• Fractional order
• Economic and environmental
• Scaled conjugate gradient
• Reference solutions
• Neural networks