Families of congruences for fractional partition functions modulo powers of primes

Recently, Chan and Wang studied the fractional partition function and found several infinite classes of congruences satisfied by the corresponding coefficients. In this paper, we find new families of congruences modulo powers of primes using the Rogers-Ramanujan continued fraction and some dissection formulae of certain q-products. We also find analogous congruences in the coefficients of the fractional powers of the generating function for the 2-color partition function.