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Modeling and analysis fractal order cancer model with effects of chemotherapy

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  • Xu, Changjin
  • Farman, Muhammad
  • Akgül, Ali
  • Nisar, Kottakkaran Sooppy
  • Ahmad, Aqeel

Abstract

In the study, the sudden act of the cancer model was studied utilizing the fractional operator and its applications to discretize the conformable cancer model. A collection of nonlinear fractional differential equations make up the fractional-order model. We also look at the fractional-order model, which examines how chemotherapeutic attention medications, when combined, interact with the immune system and cancer cells. Both qualitative and quantitative research has been conducted on the cancer model. The proposed fractional-order cancer model's first and second derivatives of Lyapunov stability, positivity, and boundedness are all checked using nonlinear analysis. A generalized Mittag Leffler kernel is used through the ABC derivative, which is also used to check the dynamical behavior of the model. Also, utilizing alternative dimensions of fractional order and validating the effect of fractional parameters, a comparison was made to check the efficiency of the scheme for all compartments. Finally, the physiological results are analyzed and showing off is scooped up to demonstrate cancer disease and corroborate logical findings, which will be useful for future study and reducing cancer's social effect.

Suggested Citation

  • Xu, Changjin & Farman, Muhammad & Akgül, Ali & Nisar, Kottakkaran Sooppy & Ahmad, Aqeel, 2022. "Modeling and analysis fractal order cancer model with effects of chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005355
    DOI: 10.1016/j.chaos.2022.112325
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    References listed on IDEAS

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    1. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    4. Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    5. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    6. Rihan, F.A. & Abdel Rahman, D.H. & Lakshmanan, S. & Alkhajeh, A.S., 2014. "A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 606-623.
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    Cited by:

    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Sajjad, Assad & Farman, Muhammad & Hasan, Ali & Nisar, Kottakkaran Sooppy, 2023. "Transmission dynamics of fractional order yellow virus in red chili plants with the Caputo–Fabrizio operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 347-368.
    3. Hamzeh Zureigat & Mohammed Al-Smadi & Areen Al-Khateeb & Shrideh Al-Omari & Sharifah Alhazmi, 2023. "Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells," IJERPH, MDPI, vol. 20(4), pages 1-13, February.
    4. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    5. Nisar, Kottakkaran Sooppy & Farman, Muhammad & Hincal, Evren & Shehzad, Aamir, 2023. "Modelling and analysis of bad impact of smoking in society with Constant Proportional-Caputo Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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