yes there is.
tactical and logistic slot can increased planet specific with the respective upgrades. the type of planet dictates how many upgrades and this how many slots in total you can have. desert planets have the most logistics slots, terran planets also have quite a bit, the come ice and volcanic worlds and asteroids have least.
there is also a tech for tec which increases logistics slots throughout your empire and a tech for advent that increases tactical slots throughout your empire. but as I said, the primary means it on the planet level.
as for fleet size, it is increase solely via research. in the third tab in the research screen, the bottom row indicates the levels of fleet supply you can research. but be careful, every additional level increases the amount of resources lost to maintenance of fleet and fleet structures and it depends on the level researched, not on the amount actually used. so think about whether you really need and you can really afford the next level before you proceed. the first few levels though are rarely a big deal though.
edit: oh yes, and the vasari have a tech that gives them a bonus to fleet supply.
