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A Solution to the Fundamental Linear Fractional Order Differential EquationThis paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub 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 elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
Document ID
19990041952
Document Type
Technical Publication (TP)
Authors
Hartley, Tom T. (Akron Univ. Akron, OH United States)
Lorenzo, Carl F. (NASA Lewis Research Center Cleveland, OH United States)
Date Acquired
September 6, 2013
Publication Date
December 1, 1998
Subject Category
Mathematical and Computer Sciences (General)
Report/Patent Number
E-11408
NAS 1.60:208693
NASA/TP-1998-208693
Funding Number(s)
PROJECT: RTOP 523-22-13
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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