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We consider a model where massive static spherically symmetric black hole, inthe presence of power-Yang-Mills source, is surrounded by a dark fluid withnon-linear equation of state. In this set up we construct a new class ofmagnetized Lovelock black hole solutions of the gravitational field equations.In particular, we work out the metric functions in both D-dimensional massiveEinstein and massive Gauss-Bonnet gravities. We study thermodynamics of theseblack holes also and show that the mass and associated thermodynamic quantitieslike Hawking temperature and heat capacity depend on parameters of the darkfluid and the power-Yang-Mills magnetic source. We note that the entropy doesnot satisfy the area law in Gauss-Bonnet and higher order Lovelock black holes.Furthermore, phase transitions of black holes in each case are also discussed.

Lovelock black holes surrounded by dark fluid in power-Yang-Mills massive gravity