Introduction to Fractional Calculus

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Can we get nth derivatives, where n is not an integer?

This question is nearly as old as calculus itself, being first asked by Leibniz in 1695.

In the first talk in this introduction to what is usually called fractional calculus, we will ask how far we can generalise the order of differentiation, beyond Z, to R, C, and further still.

In the second talk, we will look at what theorems from integer-order calculus we can generalise, and we will employ fractional calculus (or to use a preferable term, analytic calculus) to derive a formula for the Riemann zeta function, and thus an equivalent expression for the Riemann Hypothesis, in terms of Euler’s gamma function.