Fractional trigonometry and the spiral functions

Nonlinear Dynamics

Volumn 38, Issue 1-4, 2004, Pages 23-60

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

^a NASA GLENN RESEARCH CENTER   (United States)

^b University of Akron   (United States)

Author keywords

Fractional calculus; Fractional differential equations; Fractional Euler equation; Fractional semi Euler equation; Fractional trigonometric functions; Fractional trigonometry; R function; Spiral functions

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; LAPLACE TRANSFORMS; NONLINEAR SYSTEMS; TRIANGULATION;

FRACTIONAL CALCULUS; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL EULER EQUATION; FRACTIONAL SEMI-EULER EQUATION; FRACTIONAL TRIGONOMETRIC FUNCTIONS; FRACTIONAL TRIGONOMETRY; R-FUNCTION; SPIRAL FUNCTIONS;

FUNCTIONS;

EID: 15544380308     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3745-9     Document Type: Conference Paper

References (11)

1. Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, Inc, San Diego, California, 1974.
2. Lorenzo, C. F. and Hartley, T. T., 'Generalized Functions for the Fractional Calculus, ' NASA/TP-1999-209424, October, 1999.
3. Hartley, T. T. and Lorenzo, C. F., 'A Solution to the Fundamental Linear Fractional Order Differential Equation, ' NASA/ TP-1998-208693, December, 1998.
4. Hartley, T. T. and Lorenzo, C. F., 'Dynamics and control of initialized fractional-order systems, ' Nonlinear Dynamics 29(1-4), 2002, 201-233.
5. Rabotnov, Y. N., Tables of a Fractional Exponential Function of Negative Parameters and its Integral, Nauka, Russia, 1969 [in Russian].
6. Rabotnov, Y. N., Elements of Hereditary Solid Mechanics, MIR Publishers, Moscow, 1980.
7. Lorenzo, C. F. and Hartley, T. T., 'R-Function Relationships for Application in the Fractional Calculus, ' NASA/TM-2000-210361, 2000.
8. Churchill, R. V., Complex Variables and Applications, McGraw-Hill, New York, 1960.
9. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, California, 1999.
10. Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
11. Rees, M. J., and Silk, J., The Origin of Galaxies, Cosmology+ 1, Readings from Scientific American, W. H. Freeman, New York, 1977.