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Analytical study of a modified-ABC fractional order breast cancer model

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Abstract

This study investigates breast cancer dynamics using modified ABC-fractional operators. We examine interactions among cancer stem cells, tumor cells, healthy cells, excess estrogen effects, and immune cells. By applying the “Localization of Compact Invariant Sets” technique and comparison theory, we establish conditions for cancer persistence without immune cells and eradication with an immune response. We analyze equilibria, global attraction persistence state, stability, solution uniqueness, and existence using recursive sequences and fixed point theorem. Numerical simulations with Lagrange’s interpolation validate and deepen our understanding of breast cancer dynamics. Incorporating modified ABC-fractional derivatives enhances our comprehension of the model.

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research and Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number: ISP23-86.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia

    Khaled A. Aldwoah

  2. Department of Mathematics, Hajjah University, Hajjah, Yemen

    Mohammed A. Almalahi

  3. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, 71491, Tabuk, Saudi Arabia

    Manel Hleili

  4. Department of General Studies, University of Prince Mugrin (UPM), 42311, Madinah, Saudi Arabia

    Faez A. Alqarni

  5. Department of Mathematics, College of Science, Jazan University, P.O. Box 114, 45142, Jazan, Saudi Arabia

    Elkhateeb S. Aly

  6. Nanotechnology Research Unit, College of Science, Jazan University, P.O. Box 114, Jazan, 45142, Saudi Arabia

    Kamal Shah

  7. Department of Mathematics, University of Malakand, Chakdara, Dir (Lower), Khyber Pakhtunkhawa, 18000, Pakistan

    Kamal Shah

  8. Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

    Kamal Shah

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  1. Khaled A. Aldwoah
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  2. Mohammed A. Almalahi
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  5. Elkhateeb S. Aly
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All authors contributed equally to this work.

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Correspondence to Elkhateeb S. Aly.

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Aldwoah, K.A., Almalahi, M.A., Hleili, M. et al. Analytical study of a modified-ABC fractional order breast cancer model. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02102-7

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  • DOI: https://doi.org/10.1007/s12190-024-02102-7

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