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- Tom T. Hartley, Carl F. Lorenzo
- Critical reviews in biomedical engineering
- 2008

This paper provides a solution to the fundamental linear fractional order differential equation, namely, cdtqx(t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is… (More)

- Carl F. Lorenzo, Tom T. Hartley
- Critical reviews in biomedical engineering
- 2007

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and… (More)

- Carl F. Lorenzo, Tom T. Hartley
- Critical reviews in biomedical engineering
- 2008

Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the Lead Center for NASA's scientific and technical information.… (More)

- Tom T. Hartley, Carl F. Lorenzo
- Signal Processing
- 2003

- Carl F. Lorenzo, Tom T. Hartley
- Critical reviews in biomedical engineering
- 2008

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional… (More)

- Jay L. Adams, Robert J. Veillette, Tom T. Hartley
- Signal, Image and Video Processing
- 2012

- Rick J. Lalonde, Tom T. Hartley, J. Alexis De Abreu Garcia
- IEEE Trans. Industrial Electronics
- 1993

- John B. Yerashunas, J. Alexis De Abreu Garcia, Tom T. Hartley
- IEEE Trans. Contr. Sys. Techn.
- 2003

- Tom T. Hartley, Faramarz Mossayebi
- Journal of Circuits, Systems, and Computers
- 1993

- Arjuna Madanayake, Chamith Wijenayake, +5 authors Tokunbo Ogunfunmi
- ISCAS
- 2012