Non-Uniform Bounds in Local Limit Theorems in Case of Fractional Moments
  Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$, where $s$ may be noninteger. 
S.G. Bobkov, G.P. Chistyakov, F. G\"otze
math.PR