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Critical Reviews™ in Biomedical Engineering
SJR: 0.26 SNIP: 0.375 CiteScore™: 1.4

ISSN 印刷: 0278-940X
ISSN オンライン: 1943-619X

Critical Reviews™ in Biomedical Engineering

DOI: 10.1615/CritRevBiomedEng.v36.i1.30
pages 23-38

A Solution to the Fundamental Linear Fractional Order Differential Equation

Tom T. Hartley
Department of Electrical and Computer Engineering, University of Akron, USA
Carl F. Lorenzo
National Aeronautics and Space Administration, Glenn Research Center, Cleveland, Ohio, USA

要約

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 elucidated and a simple example, the inductor terminated semi-infinite lossy line, is used to demonstrate the theory.


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