Best Decision-Making on the Stability of the Smoke Epidemic Model via Z-Numbers and Aggregate Special Maps

Abstract

The present paper considers a fractional-order smoke epidemic model. We apply fuzzy systems and probability theory to make the best decision on the stability of the smoking epidemic model by using a new class of controllers powered by special functions to effectively generalize Ulam-type stability problems. Evaluation of optimal controllability and maximal stability is the new issue. This different concept of stability not only covers the old concepts but also investigates the optimization of the problem. Finally, we apply a new optimal method for the governing model with the Atangana–Baleanu–Caputo fractional derivative to obtain stability results in Banach spaces.