Initialization of fractional-order operators and fractional differential equations

Journal of Computational and Nonlinear Dynamics

Volumn 3, Issue 2, 2008, Pages

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

^a NASA GLENN RESEARCH CENTER   (United States)

^b The University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DERIVATIVES; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); INTEGRAL EQUATIONS; LAPLACE TRANSFORMS;

FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL INTEGRALS; FRACTIONAL OPERATORS; TIME-VARYING FUNCTIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 47249104351     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2833585     Document Type: Article

References (14)

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2. Davis, H. T., 1936, The Theory of Linear Operators, Principia, Bloomington, IN.
3. Lorenzo, C. F., and Hartley, T. T., 1998, "Initialization, Conceptualization, and Application in the Generalized Fractional Calculus," NASA TP-1998-208415.
4. Lorenzo, C. F., and Hartley, T. T., 2000, "Initialized Fractional Calculus," Int. J. Appl. Math Comput. Sci., 3(3), pp. 249-266.
5. Lorenzo, C. F., and Hartley, T. T., 2001, "Initialization in Fractional-Order Systems," European Control Conference, Porto, Portugal, Sept. 4-7.
6. Ortigueira, M. D., 2003, "On the Initial Conditions in Continuous-Time Fractional Linear Systems," Signal Process., 83(11), pp. 2301-3218.
7. Hartley, T. T., and Lorenzo, C. F., 2002, "Dynamics and Control of Initialized Fractional-Order Systems," Nonlinear Dyn., 29(1-4), pp. 201-233.
8. Lorenzo, C. F., and Hartley, T. T., 2007, "Initialization of Fractional Differential Equations: Background and Theory," Proceedings of IDETC/CIE, DETEC2007-34810.
9. Lorenzo, C. F., and Hartley, T. T., 2007, "Initialization of Fractional Differen-Transactions Equations: Theory and Applications," Proceedings of IDET/CIE, DETEC2007-34814.
10. Erdelyi, A., Oberhettinger, F., and Tricomi, F. G., 1954, Tables of Integral Transforms, Bateman Manuscript Project, McGraw-Hill, p. 137.
11. Spanier, J., and Oldham, K., 1987, An Atlas of Functions, Hemisphere, New York, Springer-Verlag, London.
12. Apostol, T. M., 1957, Mathematical Analysis, Addison-Wesley, Reading, MA, LCCC 578-8707.
13. Wylie, C. R., 1975, Advanced Engineering Mathematics, McGraw-Hill, New York.
14. Lorenzo, C. F., and Hartley, T. T., 1999, "Generalized Functions for the Fractional Calculus," NASA TP-1999-209424.