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A combination of time-scale calculus and a cross-validation technique used in Fitting and evaluating fractional models. (English) Zbl 1254.34127
The authors have wonderfully combined the fractional calculus and time scale calculus to solve and fit modeling of one compartmental model for drug concertration overtime. It is a very interesting combination of one of the latest developments in Mathematics, time scale calculus as well as the age old fractional calculus. Their approach of validating their work by cross-validation technique has also given their model much merit. It is a very interesting approach that can be applied to many other physical phenomena.
MSC:
34N05Dynamic equations on time scales or measure chains
34A08Fractional differential equations
92C45Kinetics in biochemical problems
References:
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[2]Caponetto, R.; Dongola, G.; Fortuna, L.: Fractional order system: modeling and control applications, (2010)
[3]Das, S.: Functional fractional calculus for system identification and controls, (2008)
[4]Kilbas, A. A.; Srivastava, H. M.; Trujillo, Juan J.: Theory and applications of fractional differential equations, (2006)
[5]Kilbas, A. A.; Saigo, M.: Fractional integrals and derivatives of functions of Mittag-Leffler type, Dokl. akad. Nauk belarusi 39, No. 4, 22-26 (1995)
[6]Lacroix, S. F.: Traité du calcul différentiel et du calcul integral, Paris (Courcier) 3, (1819)
[7]D. Watson, Fractional Calculus and its Applications, Department of Mathematics, Mary Washington College, Fredericksburg, VA 22401, 2004.
[8]A.H Almusharff, Development of fractional trigonometry and an application of fractional calculus to pharmacokinetic model, Master Thesis, Department of Mathematics and Computer Science, Western Kentucky University, 2011.
[9]Gabrielsson, D. W.: Pharmacokinetic and pharmacodynamic data analysis: concepts and applications, (2002)
[10]Martin, Bohner; Peterson, Allan: Dynamic equations on time scale, (2001)
[11]Stone, M.: Cross-validatory choice and assessment of statistical predictions, J. R. Stat. soc. 36, No. 2, 111-147 (1974) · Zbl 0308.62063