Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine
Cancer Research Journal
Volume 6, Issue 1, March 2018, Pages: 16-19
Received: Dec. 5, 2017; Accepted: Dec. 13, 2017; Published: Jan. 12, 2018
Views 913      Downloads 69
Author
Hosein Nasrolahpour, Department of Physics, School of Sciences, Tarbiat Modares University, Tehran, Iran
Article Tools
Follow on us
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.
Keywords
Fractional Dynamics, Complex Systems, Fractional Biomechanics of Cancer Cells
To cite this article
Hosein Nasrolahpour, Fractional Dynamics of Cancer Cells and the Future of Research in Biomedicine, Cancer Research Journal. Vol. 6, No. 1, 2018, pp. 16-19. doi: 10.11648/j.crj.20180601.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).
ADDRESS
Science Publishing Group
548 FASHION AVENUE
NEW YORK, NY 10018
U.S.A.
Tel: (001)347-688-8931