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Study On The Dynamics Of A Piecewise Tumor–Immune Interaction Model

Author

Listed:
  • SAYED SAIFULLAH

    (Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan)

  • SHABIR AHMAD

    (Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan)

  • FAHD JARAD

    (Department of Mathematics, Cankaya University, Etimesgut, Ankara 06790, Turkey3Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia4Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

Abstract

Many approaches have been proposed in recent decades to represent the behaviors of certain complicated global problems appearing in a variety of academic domains. One of these issues is the multi-step behavior that some situations exhibit. Abdon and Seda devised new operators known as “piecewise operators†to deal with such problems. This paper presents the dynamics of the tumor–immune–vitamins model in the sense of a piecewise derivative. The piecewise operator considered here is composed of classical and Caputo operators. The existence and uniqueness of the solution with a piecewise derivative are presented with the aid of fixed point results. With the help of the Newton polynomial, a numerical scheme is presented for the examined model. The attained results are visualized through simulations for different fractional orders.

Suggested Citation

  • Sayed Saifullah & Shabir Ahmad & Fahd Jarad, 2022. "Study On The Dynamics Of A Piecewise Tumor–Immune Interaction Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-11, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402332
    DOI: 10.1142/S0218348X22402332
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