The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics considering the memory effect with fractional order-linear differential equation model is still limited. The current investigation seeks to solve the natural growth with memory effect in the economics model and decide the best model using fractional differential equation (FDE), namely Adomian Decomposition and Variational Iteration Methods. Also, this study assumes the level of consumer loss memory during a certain time interval denoted by a parameter (α). This study showed the model of loss memory effect with 0 < α ≤ 1 given a slowdown in output growth compared to a model without memory effect. Besides that, this study also found that output Y(t) is growing faster with the Variational Iteration method compared to the Adomian decomposition method. Also, using graphical simulation, this study found the output Y(t) is closer to the exact solution with α=0.4 and α=0.9. In conclusion, this study successfully solved natural growth with memory effect in economics and decided the best model between FDE, namely Adomian decomposition and Variational iterative methods using numerical analysis.