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In this paper, we consider Einstein gravity in the presence of a class ofnonlinear electrodynamics, called power Maxwell invariant (PMI). We take intoaccount $(2+1)$-dimensional spacetime in Einstein-PMI gravity and obtain itsblack hole solutions. Then, we regard pure $F(R)$ gravity as well as$F(R)$-conformally invariant Maxwell theory to obtain exact solutions of thefield equations with black hole interpretation. Finally, we investigate theconserved and thermodynamic quantities and discuss about the first law ofthermodynamics for the mentioned gravitational models.

Exact solutions of three dimensional black holes: Einstein gravity vs F(R) gravity