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A Stroll from the Garden of New Calculus to the New Trigonometry, or:

A Stroll from the Garden of New Calculus to the New Trigonometry, or:
WHAT IS HALF-DERIVATIVE ANYWAY?*

Carl F. Lorenzo

Glenn Research Center, NASA

Cleveland, Ohio

April 19th, 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!


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