  In the framework of Fractional Action Cosmology (FAC), we study the
generalized second law of thermodynamics for the Friedmann Universe enclosed by
a boundary. We use the four well-known cosmic horizons as boundaries namely,
apparent horizon, future event horizon, Hubble horizon and particle horizon. We
construct the generalized second law (GSL) using and without using the first
law of thermodynamics. To check the validity of GSL, we express the law in the
form of four different scale factors namely emergent, logamediate, intermediate
and power law. For Hubble, apparent and particle horizons, the GSL holds for
emergent and logamediate expansions of the universe when we apply with and
without using first law. For intermediate scenario, the GSL is valid for
Hubble, apparent, particle horizons when we apply with and without first law.
Also for intermediate scenario, the GSL is valid for event horizon when we
apply first law but it breaks down without using first law. But for power law
expansion, the GSL may be valid for some cases and breaks down otherwise.

General Physics