INVESTIGATING FRACTAL-FRACTIONAL MATHEMATICAL MODEL OF TUBERCULOSIS (TB) UNDER FRACTAL-FRACTIONAL CAPUTO OPERATOR

Haidong Qu (), Mati Ur Rahman (), Muhammad Arfan (), Ghaylen Laouini (), Ali Ahmadian, Norazak Senu and Soheil Salahshour ()
Additional contact information
Haidong Qu: Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
Mati Ur Rahman: Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, P. R. China
Muhammad Arfan: Department of Mathematics, University of Malakand, Chakdara Dir (Lower), 18000 Khyber Pakhtunkhwa, Pakistan
Ghaylen Laouini: College of Engineering and Technology, American University of the Middle East, Kuwait
Ali Ahmadian: Institute of IR 4.0, The National University of Malaysia, 43600 UKM, Bangi, Selangor, Malaysia6Department of Mathematics, Near East University, Nicosia, TRNC, Mersin 10, Turkey
Norazak Senu: Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Selangor, Malaysia
Soheil Salahshour: Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul, Turkey

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-14

Abstract: 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.

Keywords: TB Mathematical Model; Fractal-Fractional Derivative; Ulam–Hyers Stability; Fractional Adams–Bashforth Method; Simulation Results (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401260

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