Multistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kinetics

被引：1
作者：
Vosika, Z. [1 ]
Mitic, V. V. [2 ,3 ]
Vasic, A. [1 ]
Lazovic, G. [1 ]
Matija, L. [1 ]
Kocic, Lj. M. [2 ]
机构：
[1] Univ Belgrade, Fac Mech Engn, Kraljice Marije 16, Belgrade, Serbia
[2] Univ Nis, Fac Elect Engn, Aleksandra Medvedeva 14, Nish, Serbia
[3] SASA, Inst Tech Sci, Belgrade, Serbia
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 44卷
关键词：
Discrete fractional calculus; Nonlinear systems; kinetics; PARTIAL-DIFFERENTIAL-EQUATIONS;
D O I：
10.1016/j.cnsns.2016.08.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, Caputo based Michaelis-Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multistep variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：373 / 389
页数：17
相关论文
共 42 条
  • [1] On Riemann and Caputo fractional differences
    Abdeljawad, Thabet
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1602 - 1611
  • [2] Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics
    Alawneh, Ahmed
    [J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2013, 2013
  • [3] [Anonymous], 2006, THEORY APPL FRACTION
  • [4] Atici F M., 2007, International Journal of Difference Equations, V2, P165
  • [5] Modeling with fractional difference equations
    Atici, Ferhan M.
    Senguel, Sevgi
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) : 1 - 9
  • [6] Bohner M., 2001, Dynamic equations on time scales: an introduction with applications, DOI DOI 10.1007/978-1-4612-0201-1
  • [7] Bohner M., 2003, Advances in Dynamic Equations on Time Scales: An Introduction with Applications, DOI DOI 10.1007/978-0-8176-8230-9
  • [8] Model for tumour growth with treatment by continuous and pulsed chemotherapy
    Borges, F. S.
    Iarosz, K. C.
    Ren, H. P.
    Batista, A. M.
    Baptista, M. S.
    Viana, R. L.
    Lopes, S. R.
    Grebogi, C.
    [J]. BIOSYSTEMS, 2014, 116 : 43 - 48
  • [9] Cao X, 2011, JNSA, V2, P189
  • [10] Cermak J, 2011, ABSTR APPL ANAL, P22
12345