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I stumbled onto fractional calculus my sophomore
year of Undergrad during a differential equations class lecture. Distracted by
the thought, I simply asked myself what would an equation look like that allowed
for taking nth derivatives of some function. My first derivation was taking the
nth derivative of polynomials and later I worked on cyclic functions.
After deriving these equations, I wondered if they were valid for all n - even
fractional values. It turns out that they are!
Most recently, I have have been studying a publication by Igor Podlubny. In the publication, he deals with
geometric
and physical interpretations of fractional integrals and below is an example
of a geometrical interpretation of the Right Hand Riemann Liouville Fractional
Integral for alpha = 0.75 (where alpha denotes the order of integration - to see
the values of the axis examine figure 1 in the above link). To see an
animation of varying alpha that I constructed click
here.
This work has now been published. Please see
"Geometrical interpretation of
fractional integration: shadows on the walls"
on JOMA.
Animation >> Geometric
Interpretation of a Fractional Integral
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