IEEE/CAA Journal of Automatica Sinica
Citation:  Mithun Kumar Ghosh, Tridip Sardar, Xianbing Cao and Priti Kumar Roy, "Mathematical Study of A Memory Induced Biochemical System," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 11421149, Nov. 2018. doi: 10.1109/JAS.2018.7511234 
[1] 
R. Dutta, Fundamentals of Biochemical Engineering. Berlin:Springer, 2008.

[2] 
I. Belgacem and J. L. Gouzé, "Global Stability of full open reversible michaelismenten reactions, " IFAC Proc., vol. 45, no. 15, pp. 591596, 2012. https://www.researchgate.net/publication/280756540_Global_Stability_of_Full_Open_Reversible_MichaelisMenten_Reactions

[3] 
D. L. Nelson and M. M. Cox, Lehninger Principles of Biochemistry, 6th ed. Basingstoke:Macmillan Education, 2013.

[4] 
S. Sirin, D. A. Pearlman, and W. Sherman, "Physicsbased enzyme design: predicting binding affinity and catalytic activity, " Proteins: Struct. Funct. Bioinform., vol. 82, pp. 33973409, Dec. 2014. http://med.wanfangdata.com.cn/Paper/Detail?id=PeriodicalPaper_PM25243583

[5] 
D. VasicRacki, U. Kragl, and A. Liese, "Benefits of enzyme kinetics modelling, " Chem. Biochem. Eng. Quart., vol. 17, no. 1, pp. 718, Mar. 2003. https://www.researchgate.net/publication/237254930_Benefits_of_Enzyme_Kinetics_Modelling

[6] 
R. Roskoski Jr, "The ErbB/HER family of proteintyrosine kinases and cancer, " Pharmacol. Res., vol. 79, pp. 3474, Jan. 2014. http://www.sciencedirect.com/science/article/pii/S1043661813001771

[7] 
P. K. Roy, S. Datta, S. Nandi, and F. Al Basir, "Effect of mass transfer kinetics for maximum production of biodiesel from Jatropha Curcas oil: a mathematical approach, " Fuel, vol. 134, pp. 3944, Oct. 2014. http://www.sciencedirect.com/science/article/pii/S0016236114004682

[8] 
S. D. Thiberville, N. Moyen, L. DupuisMaguiraga, A. Nougairede, E. A. Gould, P. Roques, and X. De Lamballerie, "Chikungunya fever: epidemiology, clinical syndrome, pathogenesis and therapy, " Antiv. Res., vol. 99, no. 3, pp. 345370, Sep. 2013. http://www.ncbi.nlm.nih.gov/pubmed/23811281

[9] 
Y. L. Qi, D. G. Musson, B. Schweighardt, T. Tompkins, L. Jesaitis, A. J. Shaywitz, K. Yang, and C. A. O'Neill, "Pharmacokinetic and pharmacodynamic evaluation of Elosulfase Alfa, an enzyme replacement therapy in patients with morquio a syndrome, " Clin. Pharmacokinet., vol. 53, no. 12, pp. 11371147, Dec. 2014. http://europepmc.org/articles/PMC4243006

[10] 
J. D. Murray, Mathematical Biology:Ⅰ. An Introduction, 3rd ed. New York:Springer, 2002.

[11] 
L. A. Segel, Mathematical Models in Molecular and Cellular Biology. Cambridge:Cambridge University Press, 1980.

[12] 
G. Varadharajan and L. Rajendran, "Analytical solution of coupled nonlinear second order reaction differential equations in enzyme kinetics, " Nat. Sci., vol. 3, no. 6, pp. 459465, May 2011. http://www.oalib.com/paper/4765

[13] 
A. Meena, A. Eswari, and L. Rajendran, "Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of nonlinear reaction equations, " J. Math. Chem., vol. 48, no. 2, pp. 179186, Aug. 2010. doi: 10.1007/s1091000996595

[14] 
P. T. Benavides and U. Diwekar, "Optimal control of biodiesel production in a batch reactor: Part Ⅰ: deterministic control, " Fuel, vol. 94, pp. 211217, Apr. 2012.

[15] 
P. K. Roy, S. Nandi, and M. K. Ghosh, "Modeling of a control induced system for product formation in enzyme kinetics, " J. Math. Chem., vol. 51, pp. 27042717, Nov. 2013. doi: 10.1007/s109100130232x

[16] 
F. A. Basir, R. Bhattacharyya, and P. K. Roy, "Delay induced oscillation in a biochemical model and its control, " Nonlin. Stud., vol. 22, no. 3, pp. 453472, Aug. 2015. https://www.researchgate.net/publication/281549913_Delay_induced_oscillation_in_a_biochemical_model_and_its_control

[17] 
R. A. Azizyan, A. E. Gevorgyan, V. B. Arakelyan, and E. S. Gevorgyan, "Mathematical modeling of uncompetitive inhibition of Bisubstrate enzymatic reactions, " Int. Schol. Sci. Res. Innov., vol. 7, no. 10, pp. 974977, 2013. https://waset.org/Publication/mathematicalmodelingofuncompetitiveinhibitionofbisubstrateenzymaticreactions/17025

[18] 
S. Westerlund, "Dead matter has memory!, " Phys. Scrip., vol. 43, no. 2, pp. 174179, 1991. doi: 10.1088/00318949/43/2/011

[19] 
V. E. Tarasov, "Review of some promising fractional physical models, " Int. J. Mod. Phys. B, vol. 27, no. 9, pp. Article No. 1330005, Mar. 2013. doi: 10.1142/S0217979213300053

[20] 
A. A. Stanislavsky, "Memory effects and macroscopic manifestation of randomness, " Phys. Rev. E, vol. 61, no. 5, pp. 47524759, May 2000. http://www.europepmc.org/abstract/MED/11031515

[21] 
J. K. Popović, M. T. Atanacković, A. S. Pilipović, M. R. Rapaić, S. Pilipović, and T. M. Atanacković, "A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of diclofenac, " J. Pharmacokinet. Pharmacodyn., vol. 37, no. 2, pp. 119134, Apr. 2010. doi: 10.1007/s1092800991473

[22] 
R. ToledoHernandez, V. RicoRamirez, G. A. IglesiasSilva, and U. M. Diwekar, "A fractional calculus approach to the dynamic optimization of biological reactive systems. Part Ⅰ: fractional models for biological reactions, " Chem. Eng. Sci., vol. 117, pp. 217228, Sep. 2014. http://www.sciencedirect.com/science/article/pii/S0009250914003212

[23] 
E. Ahmed and A. S. Elgazzar, "On fractional order differential equations model for nonlocal epidemics, " Phys. A: Statist. Mechan. Appl., vol. 379, no. 2, pp. 607614, Jun. 2007. http://www.sciencedirect.com/science/article/pii/S0378437107000623

[24] 
M. L. Du, Z. H. Wang, and H. Y. Hu, "Measuring memory with the order of fractional derivative, " Sci. Rep., vol. 3, pp. Article No. 3431, Dec. 2013. http://www.ncbi.nlm.nih.gov/pubmed/24305503

[25] 
M. ElShahed and A. Alsaedi, "The fractional SIRC model and influenza A, " Math. Probl. Eng., vol. 2011, pp. Article No. 480378, Aug. 2011. http://www.ams.org/mathscinetgetitem?mr=2853306

[26] 
S. Abbas, M. Benchohra, G. M. NǴuérékata, and B. A. Silmani, "Darboux problem for fractionalorder discontinuous hyperbolic partial differential equations in Banach algebras, " Compl. Variabl. Elliptic Equat.:Int. J., vol. 57, no. 24, pp. 337350, 2012. doi: 10.1080/17476933.2011.555542

[27] 
I. Podlubny, Fractional Differential Equations. San Diego:Academic Press, 1999.

[28] 
F. A. Abdullah, "Using fractional differential equations to model the MichaelisMenten reaction in a 2d region containing obstacles, " Science Asia, vol. 37, no. 1, pp. 7578, 2011. doi: 10.2306/scienceasia15131874.2011.37.075

[29] 
A. Alawneh, "Application of the multistep generalized differential transform method to solve a timefractional enzyme kinetics, " Discr. Dyn. Nat. Soc., vol. 2013, pp. Article No. 592938, 2013. http://d.old.wanfangdata.com.cn/OAPaper/oai_doajarticles_fc557bf0eca732bc96fd08c38dc1e6f1

[30] 
A. Dokoumetzidis, R. Magin, and P. Macheras, "Fractional kinetics in multicompartmental systems, " J. Pharmacokinet. Pharmacodyn., vol. 37, no. 5, pp. 507524, Oct. 2010. http://www.ncbi.nlm.nih.gov/pubmed/20886267

[31] 
T. Sardar, S. Rana, and J. Chattopadhyay, "A mathematical model of dengue transmission with memory, " Commun. Nonlin. Sci. Numer. Simulat., vol. 22, no. 13, pp. 511525, May 2015. http://www.sciencedirect.com/science/article/pii/S100757041400392X

[32] 
B. S. Chen, C. Y. Li, B. Wilson, and Y. J. Huang, "Fractional modeling and analysis of coupled MR damping system, " IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 288294, Jul. 2016. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=ZDHB201603009&dbname=CJFD&dbcode=CJFQ

[33] 
S. Rana, S. Bhattacharya, J. Pal, G. M. NǴuérékata, and J. Chattopadhyay, "Paradox of enrichment: a fractional differential approach with memory, " Phys. A: Statist. Mechan. Appl., vol. 392, no. 17, pp. 36103621, Sep. 2013. http://www.ams.org/mathscinetgetitem?mr=3069186

[34] 
M. K. Ghosh, J. Pal, and P. K. Roy, "How memory regulates drug resistant pathogenic bacteria? a mathematical study, " Int. J. Appl. Comput. Math., vol. 3, no. S1, pp. 747773, Dec. 2017. doi: 10.1007/s408190170339z

[35] 
V. E. Tarasov, "No violation of the Leibniz rule. No fractional derivative, " Commun. Nonlin. Sci. Numer. Simulat., vol. 18, no. 11, pp. 29452948, Nov. 2013. http://www.sciencedirect.com/science/article/pii/S1007570413001457

[36] 
M. S. Tavazoei, and M. Haeri, "Chaotic attractors in incommensurate fractional order systems, " Phys. D, vol. 237, no. 20, pp. 26282637, Oct. 2008. http://www.sciencedirect.com/science/article/pii/S0167278908001310

[37] 
S. Nandi, M. K. Ghosh, R. Bhattacharya, and P. K. Roy, "Mathematical modeling to optimize the product in enzyme kinetics, " Control Cybern., vol. 42, no. 2, pp. 431442, 2013. https://www.researchgate.net/publication/286754467_Mathematical_modeling_to_optimize_the_product_in_enzyme_kinetics?ev=auth_pub

[38] 
S. Schnell and P. K. Maini, "Enzyme kinetics at high enzyme concentration, " Bull. Math. Biol., vol. 62, no. 3, pp. 483499, May 2000. http://www.ncbi.nlm.nih.gov/pubmed/10812718

[39] 
S. Schnell and P. K. Maini, "A century of enzyme kinetics: reliability of the K_{M} and v_{max} estimates, " Comm. Theoret. Biol., vol. 8, no. 23, pp. 169187, MarJan. 2003. http://www.ingentaconnect.com/content/tandf/gctb/2003/00000008/F0020002/art00003
