Cancer Research Journal

| Peer-Reviewed |

Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine

Received: 05 December 2017    Accepted: 13 December 2017    Published: 12 January 2018
Views:       Downloads:

Share This Article

Abstract

Following our previous works on fractional biophysical issues such as fractional dynamics of protein folding process and fractional dynamics of cancer cells and their branching processes, in this work we further develop these issues and propose a new fractional biomechanics of cancer cells. In this short note we present some promising models for future studies in biomedicine, including constant and variable order fractional Maxwell and Kelvin–Voigt models to study the mechanics of cancer cells. We also emphasize that fractional calculus will play a vital and central role in the understanding of the complexities that occur when we deal with the phenomena and processes in the realm of bioscience and biomedicine and particularly in physics of cancer.

DOI 10.11648/j.crj.20180601.13
Published in Cancer Research Journal (Volume 6, Issue 1, March 2018)
Page(s) 16-19
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractional Dynamics, Complex Systems, Fractional Biomechanics of Cancer Cells

References
[1] R. Gorenflo and F. Mainardi, Fractional Calculus (Springer, 1997).
[2] H. Nasrolahpour, Prespacetime J. 2 (8) (2011) 1264-1269.
[3] H. Nasrolahpour, Prespacetime J. 2 (13) (2011) 2053-2059.
[4] H. Nasrolahpour, Prespacetime J. 3 (1) (2012) 99-108.
[5] H. Nasrolahpour, Prespacetime J. 3 (12) (2012) 1194-1196.
[6] H. Nasrolahpour, Prespacetime J. 3 (13) (2012) 1247-1250.
[7] H. Nasrolahpour, Prespacetime J. 4 (6) (2013) 604-608.
[8] V. E. Tarasov, G. M. Zaslavsky, Comm. Nonl. Sci. Num. Simul. 11 (2006) 885-898.
[9] N. Korabel et al. Comm. Nonl. Sci. Num. Simul. 12 (2007) 1405-1417.
[10] D. Baleanu et al., Nonlinear Dyn. 60 (2010) 81-86.
[11] D. Baleanu et al., Cent. Eur. J. Phys. 8(1) (2010) 120-125.
[12] Y. Luchko, J. Math. Phys. 54 (2013) 012111.
[13] S. I. Muslih et al., J. Phys. A: Math. Theor. 43 (2010) 055203.
[14] S. I. Muslih et al., Int. J. Theor. Phys. 49 (2010) 1746-1752.
[15] J. F. Gómez-Aguilar et al., Revista mexicana de física 58 (4) (2012) 348-352.
[16] J. F. Gómez-Aguilar et al., Journal of Electrical Bioimpedance 3 (1) (2012) 2-11.
[17] J. F. Gómez-Aguilar et al., Entropy 17 (9) (2015) 6289-6303.
[18] R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, 2000).
[19] J. Sabatier, et al. (Eds.), Advances in Fractional Calculus (Springer, 2007).
[20] R. Herrmann, Fractional Calculus (World Scientific Press, 2011).
[21] J. Klafter et al. (Eds.), Fractional Dynamics: Recent Advances (World Scientific, 2011).
[22] H. Nasrolahpour, Comm. Nonl. Sci. Num. Simul. 18(9) (2013) 2589–2593.
[23] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers (Springer, 2011).
[24] V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers (Springer, 2012).
[25] K. B. Oldham, J. Spanier, the Fractional Calculus (Academic Press, 1974).
[26] S. G. Samko et al., Fractional Integrals and Derivatives (Gordon and Breach, 1993).
[27] I. Podlubny, Fractional Differential Equations (Academic Press, 1999).
[28] M. Kaku, Quantum field theory, a modern introduction (Oxford University Press, 1993).
[29] M. Mathai, H. J. Haubold, Special Functions for Applied Scientists (Springer, 2008).
[30] M. Du et al., Sci. Rep. 3 (2013) 3431.
[31] A. Mvogo et al., Comm. Nonl. Sci. Num. Simul. 48 (2017) 258–269.
[32] A. Mvogo and T. C. Kofané, Chaos 26 (2016) 123120.
[33] J. A. Tenreiro Machado et al., Comm. Nonl. Sci. Num. Simul. 16 (2011) 2963–2969.
[34] H. Nasrolahpour, Fractional Field Theory Approach to Protein Folding Dynamics, bio Rxiv (2017) doi: 10.1101/153999.
[35] E. Ahmed et al, Journal of Fractional Calculus and Applications 3(2) (2012) 1- 6.
[36] F. A. Rihan et al., J. Tumor Res. 2(1) (2016) 109.
[37] X. Cao et al., J. Syst. Sci. Complex 29 (2016) 1565–1584.
[38] M. A. Moreles and R. Lainez, Commun Nonlinear Sci Numer Simulat 46 (2017) 81–88.
[39] W. Teka et al., PLOS Computational Biology 10(3) (2014) e1003526.
[40] M. Caputo and C. Cametti, Physica A 462 (2016) 705–713.
[41] Z. B. Vosika et al., PLOS ONE 8(4) (2013) e59483.
[42] C. M. A. Pinto and A. R. M. Carvalho, J. Comput. App. Math. 312 (2017) 240–256.
[43] H. Nasrolahpour, Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer, bio Rxiv (2017) doi: 10.1101/214197.
[44] V. E. Tarasov, Fractional Dynamics (Springer, 2011). V. E. Tarasov, Int. J. Mod. Phys. A 27(9) (2013) 1330005.
[45] V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers (Springer, 2012).
[46] K. B. Oldham, J. Spanier, the Fractional Calculus (Academic Press, 1974).
[47] S. G. Samko et al., Fractional Integrals and Derivatives (Gordon and Breach, 1993).
[48] I. Podlubny, Fractional Differential Equations (Academic Press, 1999).
[49] F. Mainardi, Chaos Solit. Fract. 7(9) (1996) 146.
[50] F. Mainardi et al., Fractional Calculus Appl. Anal. 4(2) (2001) 153.
[51] R. Meng et al., Applied Mathematical Modelling 40 (2016) 398–406.
[52] J. E. Palomares-ruiz et al., Revista Mexicana de Fisica 61 (2015) 261–267.
[53] N. Demirci and E. Tönük, Acta of Bioengineering and Biomechanics 16 (4) (2014) 13-21.
[54] B. Joźwiak et al., PLoS ONE (10) (2015) e0143090.
[55] B. Carmichael, Phys. Biol. 12 (2015) 046001.
[56] C. A. M. La Porta and S. Zapperi, Physics of Cancer (Cambridge University Press, 2017).
Author Information
  • Department of Physics, School of Sciences, Tarbiat Modares University, Tehran, Iran

Cite This Article
  • APA Style

    Hosein Nasrolahpour. (2018). Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine. Cancer Research Journal, 6(1), 16-19. https://doi.org/10.11648/j.crj.20180601.13

    Copy | Download

    ACS Style

    Hosein Nasrolahpour. Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine. Cancer Res. J. 2018, 6(1), 16-19. doi: 10.11648/j.crj.20180601.13

    Copy | Download

    AMA Style

    Hosein Nasrolahpour. Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine. Cancer Res J. 2018;6(1):16-19. doi: 10.11648/j.crj.20180601.13

    Copy | Download

  • @article{10.11648/j.crj.20180601.13,
      author = {Hosein Nasrolahpour},
      title = {Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine},
      journal = {Cancer Research Journal},
      volume = {6},
      number = {1},
      pages = {16-19},
      doi = {10.11648/j.crj.20180601.13},
      url = {https://doi.org/10.11648/j.crj.20180601.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.crj.20180601.13},
      abstract = {Following our previous works on fractional biophysical issues such as fractional dynamics of protein folding process and fractional dynamics of cancer cells and their branching processes, in this work we further develop these issues and propose a new fractional biomechanics of cancer cells. In this short note we present some promising models for future studies in biomedicine, including constant and variable order fractional Maxwell and Kelvin–Voigt models to study the mechanics of cancer cells. We also emphasize that fractional calculus will play a vital and central role in the understanding of the complexities that occur when we deal with the phenomena and processes in the realm of bioscience and biomedicine and particularly in physics of cancer.},
     year = {2018}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine
    AU  - Hosein Nasrolahpour
    Y1  - 2018/01/12
    PY  - 2018
    N1  - https://doi.org/10.11648/j.crj.20180601.13
    DO  - 10.11648/j.crj.20180601.13
    T2  - Cancer Research Journal
    JF  - Cancer Research Journal
    JO  - Cancer Research Journal
    SP  - 16
    EP  - 19
    PB  - Science Publishing Group
    SN  - 2330-8214
    UR  - https://doi.org/10.11648/j.crj.20180601.13
    AB  - Following our previous works on fractional biophysical issues such as fractional dynamics of protein folding process and fractional dynamics of cancer cells and their branching processes, in this work we further develop these issues and propose a new fractional biomechanics of cancer cells. In this short note we present some promising models for future studies in biomedicine, including constant and variable order fractional Maxwell and Kelvin–Voigt models to study the mechanics of cancer cells. We also emphasize that fractional calculus will play a vital and central role in the understanding of the complexities that occur when we deal with the phenomena and processes in the realm of bioscience and biomedicine and particularly in physics of cancer.
    VL  - 6
    IS  - 1
    ER  - 

    Copy | Download

  • Sections