  A time-changed fractional mixed fractional Brownian motion by inverse alpha
stable subordinator with index alpha in (0, 1) is an iterated process L
constructed as the superposition of fractional mixed fractional Brownian motion
N(a, b) and an independent inverse {\alpha}-stable subordinator Talpha. In this
paper we prove that the process LT alpha(a, b) is of long range dependence
property under a smooth condition on the Hirsh index H1 and H2. We deduce that
the fractional mixed fractional Brownian motion has long range dependence for
every H1 < H2.
