The computation of fractional order differential and integration equations is highly utilized in numerous fields, such as mathematics in biology, ecology, physics, chemistry, and so on. This article aims at presenting methods for analytical and numerical solutions, Lie’s symmetry analysis, computing conservation laws for Burger’s fractional order differential equation (FODE), and reducing time-fractional cylindrical-Burgers equation order. Hence, we have employed a generalized (G′/G) expansion method for analytical solutions and a non-standard finite difference scheme for numerically solving Burger’s FODE. Additionally, the fractional derivative generalization of Noether's theorem has been utilized to compute the equation’s conservation laws. Numerical results have been reported here to approve theoretical results acquired in non-standard finite difference schemes. The proposed generalized (G′/G) expansion method is a simple, accurate, and practical approach to problem solving. Additionally, this method can be employed to execute non-linear wave equations. Programs including MATLAB and Maple have been utilized to simplify the process of solving complex equations.