Unemployment Dynamics Using Multi-Order Fractional Mathematical Model: A Case Study Of Northern States Of India

The continuous increase in unemployment rates and their significant economic impact necessitate the rapid updating and modification of present models and policies implemented by governmental entities. To successfully handle the timely transmission of employment within the workforce, many contemporary models still need the incorporation of an individual’s job history. Consequently, in order to study the unemployment problem, this research presents a multi-order fractional nonlinear mathematical model that takes into account the Caputo fractional order derivative and three important variables: the number of skilled unemployed individuals, the number of employed individuals, and the number of open positions. The existence and uniqueness of the proposed model’s solution are demonstrated by using generalization of Picard fixed point theorem. The solution of the proposed model is bounded and non-negative. The reproduction number has been analyzed to determine the factors that would help create new job vacancies. The multi-order model utilizes real data to make predictions regarding the unemployed as well as the employed population for the Northern states of India (J&K, HP, Punjab, Haryana) with an average absolute error less than 21% and 3%, respectively. When compared to the actual data, the fractional order model better captures the characteristics of the unemployed population than the integer order model. The fractional-order model exhibits lower RMSE, MAE and MAPE values and higher correlation coefficient (r) value.