Comparative Study of the Fractional-Order Crime System as a Social Epidemic of the USA Scenario

Abstract

Fractional derivatives are considered significant mathematical tools to design the fractional-order models of real phenomena. In this investigation, we are going to design and compare the non-integer models of the crime system by using three fractional-order operators called Atangana-Baleanu-Caputo, Caputo, and Caputo-Fabrizio derivatives for the first time. We use the real initial conditions for the subgroups of USA. To get the approximate solutions of the suggested models some numerical methods are derived. To see the performance of the numerical methods different values of the fractional orders are considered. The differences between the solutions under the used operators for each state variable are provided through some figures.

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