This study presents a novel fractional order grey model FGM(α,1)obtained by extending the grey model(GM(1,1)).For this,we generalize the whitenization first-order differential equation to fractional order by using th...This study presents a novel fractional order grey model FGM(α,1)obtained by extending the grey model(GM(1,1)).For this,we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of orderα.A real-world case study,scrutinize the economic growth influence on environmental degradation in Turkey,is performed to evaluate the significance of the projected model FGM(α,1)in contrast to the current classical GM.We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and shortrun relation among economic growth,agriculture,forestry and fishing(AFF),electricity utilization and CO_(2)emissions.Using the new fractional order model,all the variables are forecasted in the forthcoming years until 2030.Findings disclose that electricity utilization and economic growth(GDP)accelerate emission of CO_(2) though in the long run agriculture,forestry,and fishing reduce the environmental pollution in Turkey.展开更多
In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the ...In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed.Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models.We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.展开更多
文摘This study presents a novel fractional order grey model FGM(α,1)obtained by extending the grey model(GM(1,1)).For this,we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of orderα.A real-world case study,scrutinize the economic growth influence on environmental degradation in Turkey,is performed to evaluate the significance of the projected model FGM(α,1)in contrast to the current classical GM.We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and shortrun relation among economic growth,agriculture,forestry and fishing(AFF),electricity utilization and CO_(2)emissions.Using the new fractional order model,all the variables are forecasted in the forthcoming years until 2030.Findings disclose that electricity utilization and economic growth(GDP)accelerate emission of CO_(2) though in the long run agriculture,forestry,and fishing reduce the environmental pollution in Turkey.
基金This research is supported by the Scientific and Technological Research Council of Turkey(TUBTAK)under the Grant No.TBAG-117F473.
文摘In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed.Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models.We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.
