Initialization of fractional differential equations: Background and theory

2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007

Volumn 5 PART B, Issue , 2008, Pages 1325-1333

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

^a NASA GLENN RESEARCH CENTER   (United States)

^b UNIVERSITY OF AKRON   (United States)

Author keywords

Fractional differential equations; Fractional operators; Initialization; Laplace transforms

Indexed keywords

(E ,2E) THEORY; (E ,3E) PROCESS; DERIVATIVE OPERATORS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL INTEGRALS; FRACTIONAL OPERATORS; HIGHER ORDER; INTERNATIONAL CONFERENCES; INTERNATIONAL DESIGNS; MULTI-BODY SYSTEM (MBS); NON-LINEAR DYNAMICS; TECHNICAL CONFERENCES; TIME-VARYING FUNCTIONS;

ARCHITECTURAL DESIGN; BESSEL FUNCTIONS; COMPUTER CONTROL; COMPUTER NETWORKS; COMPUTERS; CONTROL SYSTEMS; DERIVATIVES; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DYNAMICAL SYSTEMS; DYNAMICS; ENGINEERING; EXTRAPOLATION; FUNCTION EVALUATION; INFORMATION SYSTEMS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL MORPHOLOGY; MECHANICS; NONLINEAR PROGRAMMING; PAPER; TECHNOLOGY;

DIFFERENCE EQUATIONS;

EID: 44849094861     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2007-34810     Document Type: Conference Paper

References (11)

1. Oldham, K B. and Spanier, J, The Fractional Calculus Mathematics in Science and Engineering, Vol. Ill, ISBN 012-525550-0, Academic Press, 1974.
2. Lorenzo, C. F. and Hartley, T. T., "Initialization, Conceptualization, and Application in the Generalized Fractional Calculus," NASA TP-1998-208415, Dec. 1998.
3. Lorenzo, C. F. and Hartley, T. T., "Initialized Fractional Calculus," International Journal of Applied Mathematics, Vol.3, No. 3 September, 2000, pp.249-266.
4. Lorenzo, C. F. and Hartley, T. T., "Initialization in Fractional-Order Systems," European Control Conference, September 4-7,2001, Porto, Portugal.
5. Ortigueirra, M. D., "On the Initial Conditions in Continuous-Time Fractional Linear Systems", Signal Processing, Vol. 83,No. 11, pp.2301-3218, Nov. 2003.
6. Hartley, T. T. and Lorenzo, C. F. "Dynamics and Control of Initialized Fractional-Order Systems," Journal of Nonlinear Dynamics, Special Journal on Fractional Calculus Vol. 29, Nos 1-4, 201-233, July 2002.
7. Erdelyi, A., Oberhettinger, F., and Tricomi, F. G., Tables of Integral Transforms, Bateman Manuscript Project, McGraw-Hill Book Co, 1954, p. 137
8. Apostol, T. M., Mathematical Analysis, LCCC 578-8707, Addison Wesley, 1957
9. Spanier, J. and Oldham, K., An Atlas of Functions, Hemisphere Pub. Corp. New York & Springer-Verlag, London, ISBN 0-89116-573-8, 1987
10. Wylie, C. R., Advanced Engineering Mathematics, ISBN 07-072180-7, McGraw-Hill, 1975
11. Lorenzo, C. F. and Hartley, T. T., "Initialization of Fractional Differential Equations: Theory and Application" DETEC2007-34810 Proceedings of IDETC/CIE, 2007