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A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative

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  • Ghanbari, Behzad
  • Kumar, Sunil
  • Kumar, Ranbir

Abstract

Mathematical biology is one of the interesting research area of applied mathematics that describes the accurate description of phenomena in biology and related health issues. The use of new mathematical tools and definitions in this area of research will have a great impact on improving community health by controlling some diseases. This is the best reason for doing new research using the latest tools available to us. In this work, we will make novel numerical approaches to the immunogenetic tumour model to using differential and integral operators with Mittag-Leffler law. To be more precise, the fractional Atangana- Baleanu derivative has been utilized in the structure of proposed model. This paper proceeds by examining and proving the convergence and uniqueness of the solution of these equations. The Adam Bashforth’s Moulton method will then be used to solve proposed fractional immunogenetic tumour model. Numerical simulations for the model are obtained to verify the applicability and computational efficiency of the considered process. Similar models in this field can also be explored similarly to what has been done in this article.

Suggested Citation

  • Ghanbari, Behzad & Kumar, Sunil & Kumar, Ranbir, 2020. "A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300187
    DOI: 10.1016/j.chaos.2020.109619
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    10. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    11. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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    13. Ghanbari, Behzad & Cattani, Carlo, 2020. "On fractional predator and prey models with mutualistic predation including non-local and nonsingular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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