Productivity with Fatigue and Long Memory: Fractional Calculus Approach

Abstract

The modeling of fatigue and long memory processes under the physical and intellectual work of individual employees and a group of employees is considered. Mathematical models of productivity that take into account long memory and fatigue among employees are suggested. In these models we assume that workers remember how the work proceeded earlier, and we take into account the impact of these memories on the productivity at the present time. We propose equations that describe how memories of employees affect the productivity of their work. Solutions of these integro-differential equations with the Riemann–Liouville fractional integrals and the Caputo fractional derivatives of non-integral order are obtained. These solutions describe the productivity and work of employees of companies and firms.