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In this study, we present a mathematical model of socio-economic process of labor force migration. We present our model in the terms of distributed order fractional partial differential equation. The proposed model involves time varying diffusion coefficient. To solve this model we propose an implicit discrete scheme by using graded meshes, and study numerically labor migration flow data from Turkey along with other countries throughout the period of 1966–2014. [ABSTRACT FROM AUTHOR]

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 order α. 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 short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO2 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 CO2 though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey. [ABSTRACT FROM AUTHOR]