Abstract
A mathematical solution to Einstein's field equations with a perfect fluid source, with variable gravitational constant $G$ and Cosmological constant $\Lambda$ for FRW space-time in higher dimensions is obtained and case study has also been done where the values of $\rho(t), G(t), \Lambda(t), q(t),$ and $d_{H}(t)$ has been obtained and their nature is also analyzed.
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