Abstract

The Fokas method, or unified transform method, was developed in the late 1990s as a powerful method to solve PDEs by combining transforms with respect to both space and time, in a process which is sometimes called synthesis rather than separation of variables. It relies heavily on ideas from complex analysis, making use of Cauchy’s theorem and Jordan’s lemma to deform complex contours through regions of exponential decay. When we allow the derivatives in the PDE to be of non-integer orders, a very different problem is obtained: arguments based on polynomials no longer apply, and branch cuts in the complex plane must be taken into account. I will speak about one type of such fractional PDE , linear in 1+1 dimensions and set on the half-line, and examine how the Fokas method can be adapted to solve it. Joint work with D. Baleanu and A. S. Fokas.