Mathematical Study of Nabla Fractional Difference Tech Layoff Model

Abstract

This research aims to analyze the numerical solution and stability of the tech layoff model using the nabla difference fractional order derivative based on the Atangana–Baleanu in Caputo sense. In the analytical section of this article, we will present a novel formula for nabla fractional differences, which can be useful for obtaining stability results. Firstly, we formulate the tech layoff model and describe the problem. Secondly, we establish both the existence and uniqueness analysis by employing fixed-point techniques for the given model. We find that the projected model exists as a unique solution that adheres to the stability state of Ulam–Hyers stability conditions. Additionally, we apply a numerical scheme based on an approximate solution in a series to simulate the proposed model, employing an iterative technique. Finally, we present numerical simulations to corroborate the theoretical study. These results clearly demonstrate the notably impactful effect of the nabla difference fractional order derivative on the model behavior.