Malkus waterwheel model is a Lorenz type chaotic-physical model expressed in terms of a system of nonlinear ordinary differential equations. In this investigation, we consider fractional-order Malkus waterwheel model via Caputo type time derivative and present chaos control, anti-synchronization, numerical solutions of the fractional system. We also associate fractional-order Malkus model with two different optimal control problems. Computational results indicate that this study may serve as a framework for chaotic behavior analysis and approximate solutions of many different parametric systems. The paper may be considered as a novel contribution because optimal control formulations, numerical solutions, stability analysis for fractional-order Malkus model are studied first time in this paper. This research work may be useful for researchers concerning with chaos analysis and approximate solutions of fractional-order chaotic dynamical systems. (C) 2020 Elsevier Ltd. All rights reserved.