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Investigating Fractal-Fractional Mathematical Model Of Tuberculosis (Tb) Under Fractal-Fractional Caputo Operator

Author

Listed:
  • 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)

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.

Suggested Citation

  • Haidong Qu & Mati Ur Rahman & Muhammad Arfan & Ghaylen Laouini & Ali Ahmadian & Norazak Senu & Soheil Salahshour, 2022. "Investigating Fractal-Fractional Mathematical Model Of Tuberculosis (Tb) Under Fractal-Fractional Caputo Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-14, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401260
    DOI: 10.1142/S0218348X22401260
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