Monday 21th of November 2022, 14:00-15:00 in HG02.052
Mostafa Meliani
Fractional Calculus 101.
Fractional calculus is simply put the theory of integrals and derivatives of arbitrary order. In the
mathematical folklore, fractional calculus is traced back to a question L’Hôpital addressed in 1695 to
Leibniz inquiring him about the meaning of his (currently popular) notation \(\frac{d^n f}{dx^n}\) when \(n=1/2\). To
which Leibniz replied “. . . This is an apparent paradox from which, one day, useful consequences will
be drawn. . . . ”. Today fractional derivatives are used in many physics models, in particular to model
power law phenomena.
During this talk we will generalize the concept of integrals of integer order, and will subsequently
introduce two concurrent concepts of fractional derivatives (yes, there are many of them, maybe the
paradox Leibniz mentioned in his letter) and discuss some of their properties.