Effect of Dynamical Cosmological Constant in presence of Modified Chaplygin Gas for Accelerating Universe

In this paper we have considered the Universe to be filled with Modified Gas and the Cosmological Constant $\mathrm{\Lambda }$ to be time-dependent with or without the Gravitational Constant $G$ to be time-dependent. We have considered various phenomenological models for $\mathrm{\Lambda }$, viz., $\Lambda\propto\rho, \Lambda\propto\frac{\dot{a}^{2}}{a^{2}}$and$\Lambda\propto\frac{\ddot{a}}{a}$. Using these models it is possible to show the accelerated expansion of the Universe at the present epoch. Also we have shown the natures of $G$ and $\mathrm{\Lambda }$ over the total age of the Universe. Using the statefinder parameters we have shown the diagramamtical representation of the evolution of the Universe starting from radiation era to $\mathrm{\Lambda }$CDM model.