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In this study, we analyze complex partial differential equations, specifically focusing on nonlinear fractional-order Inviscid Burger's equations. By employing the Adomian Decomposition Method, we develop analytical approximations in the form of convergent series to solve these equations with time and space fractional derivatives in the Caputo sense. Our approach provides explicit, efficient, and highly accurate solutions, which we verify against exact solutions, eliminating the need for closure approximations and perturbation theory. We present our findings through detailed tables and graphs, offering valuable insights into the behavior of the solutions. This work advances analytical techniques and establishes a foundation for new applications in various scientific and engineering fields.