We study a viscoelastic body, in a linear stress state with fractional derivative type of dissipation. The model was formulated in [1]. Here we derive restrictions on the model that follow from Clausius-Duhem inequality. Several known constitutive equations are derived as special cases of our model. Two examples are discussed.

The research provides insight into the factors that determine absenteeism in different types of organizations, in order to facilitate the adjustment of employees and organizations in the transition process from Industry 4.0 to Industry 5.0. The aim of the study is to predict the absenteeism of employees in the context of job characteristics and mental health. Additionally, the research investigated the effect of size, ownership, and sector of the companies on absenteeism, job characteristics, and mental health. The sample included responses from 502 employees of different sociodemographic characteristics that work in various types of organizations, performing white-collar and blue-collar jobs. A short mental health questionnaire—Mental Health Inventory, MHI-5—was used in order to measure mental health. The Job Characteristics Questionnaire was used to measure the employees’ perceptions of their job characteristics—job variety, autonomy, feedback, dealing with others, task identity, and friendship. The absenteeism is operationalized with the question: “During the past 12 months, how many days were you absent from work for any reason?”. The findings suggest that mental health and job characteristics significantly reduce absenteeism among different sectors. The result showed that the size, ownership, and sector of the organization significantly affect the absenteeism, job characteristics, and the mental health of the employees. The results support the premises of Industry 5.0 and offer a new human-centric approach to absenteeism through the promotion of mental health through long-term organizational strategies and a more inclusive approach to employees’ preferences in relation to job characteristics. The study offers a new, double-sided model of absenteeism, determining causal factors from the perspective of personal and organizational factors.

A new numerical solution to the Lagrange problem is presented. The solution is compared with a priori estimates obtained recently. Also we derive a new relation that shows that the cross-sectional area at the middle of the optimally shaped column is larger than the cross-sectional area at the ends. Our numerical experiments confirm that conclusion