Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

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-NEEmodel 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.

Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems

The motive of this work is to present a computational design using the stochastic scaled conjugate gradient(SCG)neural networks(NNs)called as SCGNNs for the socio-ecological dynamics(SED)with reef ecosystems and conservation estimation.The mathematical descriptions of the SED model are provided that is dependent upon five categories,macroalgae M(v),breathing coral C(v),algal turf T(v),the density of parrotfish P(v)and the opinion of human opinion X(v).The stochastic SCGNNs process is applied to formulate the SEDmodel based on the sample statistics,testing,accreditation and training.Three different variations of the SED have been provided to authenticate the stochastic SCGNNs performance through the statics for training,accreditation,and testing are 77%,12%and 11%,respectively.The obtained numerical performances have been compared with the Runge-Kutta approach to solve the SEDmodel.The reduction of mean square error(MSE)is used to investigate the numericalmeasures through the SCGNNs for solving the SED model.The precision of the SCGNNs is validated through the comparison of the results and the absolute error performances.The reliability of the SCGNNs is performed by using the correlation values,state transitions(STs),error histograms(EHs),MSE measures and regression analysis.