Interplay of fractionality and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">PT</mml:mi></mml:math>- symmetry on a 1D lattice

We examine the stability domains of a 1D discrete Schr\"{o}dinger equation in simultaneous presence parity-time ($\cal{PT}$) symmetry and fractionality. Direct numerical examination eigenvalues system reveals that, as fractional exponent is decreased away from unity (the standard case), instability gain increases abruptly past critical value. Also, length increases, stable fraction decreases well. for fixed lattice size, an increase gain/loss also brings about abrupt gain. Finally, participation ratio modes seen to decrease with parameter exponent, evidencing tendency towards localization.