
A Stroll from the Garden of New Calculus to the New Trigonometry, or: WHAT IS HALFDERIVATIVE ANYWAY?*
Carl F. Lorenzo
Glenn Research Center, NASA
Cleveland, Ohio
April 19^{th}, 2006, 4:00pm, Manning Hall 201
Refreshments served at 3:30pm, Manning Hall 222
The mathematicians have been working on the fractional calculus almost from the time
of the invention of the calculus. So why haven't we engineers and scientists heard
much, if anything, about it? The tour begins with the ideas of fractional order integration
and differentiation, conceptualizations, and examples of where this mathematics can
be applied.
Because this mathematics generalizes the integer order calculus it is expected to
do the same for science and engineering. We will stop on our tour and visit some new
kinds of differintegrals made possible by the fractional calculus. Our stroll will
take us to the fractional trigonometry, made possible by the generalization of the
exponential function.
The fractional trigonometry creates new spiral functions that generalize the circular
functions. These spirals appear to mimic the behaviors of the galaxies and other natural
phenomena such as hurricanes and tornados. Current efforts to determine if galactic
evolution may in fact be a fractional order process will be discussed.
* Sorry, but there are no derivations on this short tour!
