  In this paper, we study thermodynamics, thermal fluctuations, phase
transitions and the charged anti-de Sitter black hole surrounded by perfect
fluid dark matter. Large black holes are shown to be stable when subject to
thermal fluctuations, and we begin by exploring how these fluctuations affect
the uncorrected thermodynamic quantities of entropy, Helmholtz free energy,
Gibbs free energy, enthalpy specific heat, and phase transition stability. We
also discuss null geodesics and the radius of the photon sphere for the charged
AdS BH and use the radius of a photon sphere to calculate the Lyapunov exponent
and angular velocity. Exceptionally, we test the effects of various parameters
of a black hole graphically by observing the existence of the correction
parameter and the coupling parameter, which reveal the behavior of corrected
thermodynamic quantities. Lastly, we see how the system is stable (under the
effects of the dark matter parameter) by figuring out the specific heat and
Hawking temperature, which are both related to entropy.
