There are no special ABAP-related solutions. SAP has been offering BW/BI for years to take the load off the main ERP system and run the reports there. Now there is HANA.
Perhaps you should work with the Basis admin to check what goes on when "certain reports" are executed? Although if these reports are the only ones with a problem then most likely it's not a database or hardware issue...
Since you didn't share the code and we can't confirm that it is as "fine tuned" as you believe it is (and this is ABAP forum), I'm not sure a lot of intelligent advice can be given here. Really, the first stop should be your Basis team and their observations / recommendations.