We study in this paper the function of development, which consists of 3 dimensions: agriculture, industry, and Human due to their strong interrelationship with each other. We will study this function in Caputo fractional non-linear model (GHD), which describe the stability relation between three dimensions. We will get the existence and uniqueness of solution and used the Banach-fixed point theorem to prove the system (GHD) has a unique fixed point and satisfies the contraction mapping. And then we get the existence equilibrium points and the stability of these points and we find the equilibrium point of (G-H) plane is locally asymptotically if R0 < 1 , i.e. The stability satisfied with the agriculture wealth and Human population, and when the three dimensions get together the system will be asymptotically stable.
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