A flat FLRW model with dynamical Λ as function of matter and geometry

•Dynamical cosmological constant as a function of both matter and geometry.•A flat FRW universe having finite time singularities.•Observational constraints on model parameters with three observational data sets H(z) + JLA + SNe Ia.•Accelerating universe with constant equation of state.•Variable cosmological constant term as a Dark energy candidate. We revisit the evolution of the scale factor in a flat FLRW spacetime with a new generalized decay rule for the dynamic Λ-term under modified theories of gravity. It analyzes certain cosmological parameters and examines their behaviours in this generalized setting which includes several decay laws in the literature. We have also obtained observational constraints on various model parameters and estimated the present values of cosmological parameters {Ωm0, ΩΛ0, q0,t0, ω0} and have discussed with various observational results. Finite time past and future singularities in this model are also discussed.