Thermodynamics in Little Rip cosmology in the framework of a type of
  f(R,T) gravity
  Cosmological reconstruction of Little Rip model in $f(R, T)$ gravity is
investigated, where $R$ is the curvature scalar and $T$ the trace of the energy
momentum tensor. The model perfectly reproduces the present stage of the
universe, characterized by the $\Lambda CDM$ model, without singularity at
future finite-time (without the Big Rip). The input parameters are determined
according to Supernovae Cosmology data and perfectly fit with the WMAP around
the Little Rip. Moreover, the thermodynamics is considered in this Little Rip
cosmology and it is illustrated that the second law of thermodynamics is always
satisfied around the Little Rip universe for the temperature inside the horizon
being the same as that of the apparent horizon. Moreover, we show the existence
of a stable fixed point in the Little Rip universe which confirms that this is
actually a late-time attractor in the phantom-dominated universe. The linear
perturbation analysis is performed around the critical points, showing that the
Little Rip model obtained is stable.
