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In this paper, the fractional-order extended Malkus-Robbins dynamo system (FOEMRD) is introduced. Additionally, the stability, complexity diagrams, Lyapunov dimension, Lyapunov exponents, and bifurcation diagrams of the system are studied. Also, we estimate the global Mittag-Leffler positive invariant sets and global Mittag-Leffler attractive sets of the proposed system. In addition, the Hamilton energy function of the FOEMRD system is computed by the Helmholtz theorem. Next, we design an energy feedback controller to control the chaos. Due to the relationship of Hamilton energy with the occurrence of chaos, the energy control method is very efficient and powerful. The applicability of the presented theories was proven with numerical simulations and related diagrams. • Presents global dynamics of the new fractional-order extended Malkus-Robbins dynamo system. • Studies global Mittag-Leffler attractive and positive invariant sets. • Calculates Hamilton energy function by using the Helmholtz theorem. • Design an energy feedback controller for the purpose of chaos control and stabilization. [ABSTRACT FROM AUTHOR]