A modified gravity theory with time-dependent exponent

In this work, we discussed the cosmological consequences of a modified gravity theory characterized by f(R) = R-n(t) where n(t) = 1 + B(t - t(0))(epsilon), B and epsilon are free parameters in the theory and a Hubble parameter which varies as H(t) = A root R where A is a real positive parameter. For some explicit and reasonable values of the free parameters of the theory, our proposal contains several novel features which were discussed in some details.