Insight into employees' perceptions on reform initiatives in public service organizations using fractional order derivatives with optimal control strategies

Gizachew Kefelew Hailu ^* Shewafera Wondimagegnhu Teklu Yohannes Fissha Abebaw Dejen Ketema Mamo

• Debre Berhan University, Debre Berhan, Ethiopia

This study presents a compartmental model that classifies employees into three categories: "indifferent," "resistiveresistant," and "adaptive," to explore their transitions based on adaptation to workplace reform initiatives. The researchers rigorously assessed the model for wellposedness and stability of its steady states. Utilizing Pontryagin's maximum principle alongside numerical simulations, the researchers identified effective strategies aimed at reducing the number of resistiveresistant employees, thereby cultivating a more supportive atmosphere for reform efforts. The findings indicate that such an environment encourages employees to remain indifferent or adaptive, fostering a positive outlook toward change. The optimal strategies identified include providing training sessions to enhance employees' skills for adapting to new processes and technologies, as well as ensuring clear communication regarding the rationale, benefits, and impacts of the reforms. Furthermore, the study examined memory effects by transforming the integer order model into a fractional order model, with graphical representations highlighting the significance of fractional derivatives in illustrating the evolution of employees' perceptions over time. This research contributes valuable insights into managing employee adaptation during organizational change.