Prof. Hanneken is a mathematical physicist working in an area called applications of fractional calculus in physics. Fractional calculus is the calculus of derivatives and integrals of non-integer order, that is, of any arbitrary real or complex order which generalizes the notions of traditional integer order derivatives and integrals.
Centuries ago, there were only integers, but when it was realized that there were numbers between the integers, the concept of real numbers expanded mathematics innumerably. Similarly, physics has been based on integer order derivatives and integrals, how will the realization of this more general calculus change physics? No one knows the answer to this yet, but it is astounding on how fast fractional calculus is finding applications.
Prof. Hanneken has published work on fractional diffusion, the fractional oscillator, the driven fractional oscillator, fractional calculus and viscoelasticity, intrinsic dissipation in fractional order systems and the time-fractional Schrodinger equation. His current interests involve the Mittag-Leffler function which is used extensively in fractional calculus.