Stieltjes moment problem via fractional moments

Stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained through maximum entropy technique, under the constraint of few fractional moments. The latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the maximum information content carried by the ordinary moments. As a consequence a model with few parameters is obtained and intrinsic numerical instability is avoided. It is proved that the approximate density is useful for calculating expected values and some other interesting probabilistic quantities.