Generalized functions for the fractional calculus

Critical Reviews in Biomedical Engineering

Volumn 36, Issue 1, 2008, Pages 39-55

  Lorenzo, Carl F ^a   Hartley, Tom T ^b  

^a NASA GLENN RESEARCH CENTER   (United States)

^b University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; FRACTIONAL CALCULUS; LAPLACE TRANSFORMATION; MATHEMATICAL PHENOMENA; MATHEMATICS; PRIORITY JOURNAL; THEORY;

ALGORITHMS; BIOPHYSICS; COMPUTER SIMULATION; MATHEMATICS; MODELS, BIOLOGICAL;

EID: 68949150967     PISSN: 0278940X     EISSN: None     Source Type: Journal    
DOI: 10.1615/CritRevBiomedEng.v36.i1.40     Document Type: Article

References (12)

1. Erdelyi, A., Editor, Magnus, W., Oberhetinger F., and Tricomi F.G., Tables of Integral Transforms, vol. 1, McGraw-Hill Book Co., 1954, LCC Number 54-6214.
2. Hartley, T.T. and Lorenzo, C.F., A Solution to the Fundamental Linear Fractional Order Differential Equation, NASA /TP - 1998-208963, December 1998.
3. Hartley, T.T. and Lorenzo, C.F., The Vector Linear Fractional Initialization Problem, NASA /TP - 1999-208919, May 1999.
4. Miller, K.S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, Inc., 1993.
5. Mittag-Leffler, M.G., Une generalisation de l'integrale de Laplace-Abel, Proc. Paris Academy of Science, pp. 537-539, March 2, 1903(a).
6. Mittag-Leffler, M.G., Sur la nouvelle fontion Eα (x), Proc. Paris Academy of Science, pp. 554-558, October 21, 1903(b).
7. Mittag-Leffler, M.G., Sur la representation analytique d'une branche uniforme d'une fonction monogene, Acta Mathematica, vol. 29, pp. 101-181, 1905.
8. Podlubny, I., Fractional Order Systems and PI Dμ Controllers, IEEE Transactions on Automatic Control, vol. 44, no. 1, January 1999.
9. Spanier, J. and Oldham, K.B., An Atlas of Functions, Hemisphere Publishing Corp. (Subsidiary of Harper & Row, Publishers Inc.) 1987.
10. Wylie, C.R., Advanced Engineering Mathematics, Fourth Edition, McGraw-Hill Book Co., 1975.
11. Robotnov, Y.N., Tables of a Fractional Exponential Function of Negative Parameters and Its Integral (in Russian), Nauka, Russia (1969).
12. Robotnov, Y.N., Elements of Hereditary Solid Mechanics (in English) MIR Publishers, Moscow, 1980.