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