Abstract
f(R,T)-gravity is a generalization of Einstein's field equations (EFEs) and f(R)-gravity. In this research article, we demonstrate the virtues of the f(R,T)-gravity model with Einstein solitons (ES) and gradient Einstein solitons (GES). We acquire the equation of state of f(R,T)-gravity, provided the matter of f(R,T)-gravity is perfect fluid. In this series, we give a clue to determine pressure and density in radiation and phantom barrier era, respectively. It is proved that if a f(R,T)-gravity filled with perfect fluid admits an Einstein soliton (g,rho,lambda) and the Einstein soliton vector field rho of (g,rho,lambda) is Killing, then the scalar curvature is constant and the Ricci tensor is proportional to the metric tensor. We also establish the Liouville's equation in the f(R,T)-gravity model. Next, we prove that if a f(R,T)-gravity filled with perfect fluid admits a gradient Einstein soliton, then the potential function of gradient Einstein soliton satisfies Poisson equation. We also establish some physical properties of the f(R,T)-gravity model together with gradient Einstein soliton.