A solution to the fundamental linear fractional order differential equation.
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.
Hartley
Tom T
TT
Department of Electrical and Computer Engineering, University of Akron, Akron, Ohio, USA. thartley@uakron.edu
Lorenzo
Carl F
CF
D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D016014:Linear Models; D008433:Mathematics; D008954:Models, Biological