Productivity with Fatigue and Long Memory: Fractional Calculus Approach

  • Valentina V. Tarasova
  • Vasily E. TarasovEmail author
Original Paper


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.


Long memory Fatigue Productivity Fractional derivative Fractional integral 

Mathematics Subject Classification

91B02 91B55 26A33 

JEL Classification

C02 E00 



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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Faculty of EconomicsLomonosov Moscow State UniversityMoscowRussian Federation
  2. 2.YandexMoscowRussian Federation
  3. 3.Skobeltsyn Institute of Nuclear PhysicsLomonosov Moscow State UniversityMoscowRussian Federation

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