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Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model

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  • Ahmed, Najma
  • Shah, Nehad Ali
  • Taherifar, Somaye
  • Zaman, F.D.

Abstract

In this article, the fractional models of cancer tumor are studied using the Laplace transform and numerical inversion. The generalized model with Caputo time-fractional derivative is considered for two different cases of the killing rate of the cancer cells. The models based on the time-fractional derivatives give a better description of the tumor evolution because, in such models, the history of the tumor cells concentration influences the time evolution of the tumor. To solve the initial-boundary value problems, some adequate transforms of variables and functions have been considered, together with the Laplace transform and the Bessel equation. A numerical method, namely the Stehfest's algorithm is used to determine the inverse Laplace transforms. The effect of fractional parameter on the tumor cells concentration has been highlighted by numerical simulations and graphical illustrations. The time variation of tumor cell concentration and its dependence of the memory parameter could provide useful information in choosing an appropriate treatment.

Suggested Citation

  • Ahmed, Najma & Shah, Nehad Ali & Taherifar, Somaye & Zaman, F.D., 2021. "Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100103x
    DOI: 10.1016/j.chaos.2021.110750
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    1. Sébastien Benzekry & Clare Lamont & Afshin Beheshti & Amanda Tracz & John M L Ebos & Lynn Hlatky & Philip Hahnfeldt, 2014. "Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-19, August.
    2. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    3. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2019. "A fractional mathematical model of breast cancer competition model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 38-54.
    5. Cecilia Suarez & Felipe Maglietti & Mario Colonna & Karina Breitburd & Guillermo Marshall, 2012. "Mathematical Modeling of Human Glioma Growth Based on Brain Topological Structures: Study of Two Clinical Cases," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-11, June.
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    1. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.

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