This paper reviews some properties of the gamma function, particularly the incomplete gamma function and its complement, as a function of the Laplace variable . The utility of these functions in the solution of initialization problems in fractional-order system theory is demonstrated. Several specific differential equations are presented, and their initialization responses are found for a variety of initializations. Both the time-domain and Laplace-domain solutions are obtained and compared. The complementary incomplete gamma function is shown to be essential in finding the Laplace-domain solution of a fractional-order differential equation.
Issue Section:
Mathematical Theory
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,” Proceedings of IDETC∕CIE 2007, ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Sept. 4–7, Las Vegas, NV, Paper No. DETC2007-34814.Copyright © 2008
by American Society of Mechanical Engineers
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