Reconstruction and stability of f(R,T) gravity with Ricci and modified Ricci dark energy

We take the Ricci and modified Ricci dark energy models to establish a connection with f(R,T) gravity, where R is the scalar curvature and T is the trace of the energy-momentum tensor. The function f(R,T) is reconstructed by considering this theory as an effective description of these models. We consider a specific model which permits the standard continuity equation in this modified theory. It is found that f(R,T) functions can reproduce expansion history of the considered models which is in accordance with the present observational data. We also explore the Dolgov-Kawasaki stability condition for the reconstructed f(R,T) functions.