Investigating fractal-fractional mathematical model of tuberculosis TB under fractal-fractional caputo operator

• Main Authors: Qu, Haidong, Ur Rahman, Mati, Arfan, Muhammad, Laouini, Ghaylen, Ahmadian, Ali, Senu, Norazak
• Format: Article
• Published: World Scientific Publishing 2022
• Online Access: http://psasir.upm.edu.my/id/eprint/101975/; https://www.worldscientific.com/doi/10.1142/S0218348X22401260

This paper discussed a new operator known as a fractal-fractional (FF), considered in the Caputo sense. We have investigated the fractional mathematical model of Tuberculosis (TB) disease under FF Caputo derivative. We have provided the existence and uniqueness for the appropriate system by using Banach and Leray–Schauder theorem and for the stability of the model, we have used the Ulam–Hyers approach. Applying the methods of basic theorems of FF calculus (FFC) and the iterative numerical techniques of fractional Adams–Bashforth method for approximate solution. For the simulation of the model, we have considered different values for fractional order α and fractal dimension β and compared the results with integer order for real data. The FFC technique is applied as a beneficial technique to know about the real-world problem and also to control the whole world situation of the aforesaid pandemic in the different continents and territories of the world. This new operator, FF in the form of Caputo derivative, gives better results than ordinary integer order. Several results have been discussed by taking the different fractal dimensions and arbitrary order.