Exploring the role of fractal-fractional operators in mathematical modelling of corruption

Abstract

In the proposed manuscript, we present a novel mathematical model for analysing the persistence of corruption in human communities, based on fractal-fractional concepts and the Mittag-Leffler kernel law. Corruption is considered analogous to a disease that can spread and influence others who are free from corruption. Our model evaluates the equilibrium points of corruption and tests their stability using the corruption reproduction number. We also apply the fixed point theory concept to check for the existence and uniqueness of a solution, in the context of a fractional fractal operator. Solution stability is verified using the perturbed Ulam Hyers technique, and an approximate solution is obtained through the use of Lagrangian polynomials. To test the validity of our model, we simulate all compartments at different fractional orders and time durations, providing additional insights into the dynamics of corruption beyond natural orders.