Computational Framework for Numerical Simulation of Fractional-Order Financial Crime Model via Lucas Collocation Technique

The Lucas collocation approach is used in this study to approximate a fractional-order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned. These dynamics are represented by a nonlinear system of five fractional differential equations in the model. For function approximations and their fractional derivatives, we use the Lucas collocation method using operational matrices. In order to obtain the necessary Lucas collocation coefficients, this method reduces the problem to a discrete system and solves it using quasi-Newton Broyden’s iterative method. Our results, which are backed by computed error bounds and evaluated residual errors, show that this approach provides more accuracy than conventional methods. By offering precise insights into how financial crime changes over time, this method improves the creation of successful crime prevention programs. We further illustrate the precision and stability benefits of our approach by contrasting it with other methods.