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Brandon H. McNaughton >> Fractional Calculus
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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