  We examine a fractional Discrete Nonlinear Schrodinger dimer, where the usual
first-order derivative of the time evolution is replaced by a non integer-order
derivative. The dimer is nonlinear (Kerr) and PT -symmetric, and we examine the
exchange dynamics between both sites. By means of the Laplace transformation
technique, the linear PT dimer is solved in closed form in terms of
Mittag-Leffler functions, while for the nonlinear regime, we resort to
numerical computations using the direct explicit Grunwald algorithm. In
general, the main effect of the fractional derivative is the onset of a
monotonically decreasing time envelope for the amplitude of the oscillatory
exchange. In the presence of PT symmetry, the dynamics shows damped
oscillations for small gain/loss in both sites, while at higher gain/loss
parameter values, the amplitudes of both sites grows unbounded. In the presence
of nonlinearity, selftrapping is still possible although the trapped fraction
decreases as the nonlinearity is increased past threshold, in marked contrast
with the standard case.
