The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than 105 variables are involved in the complexity of the weather system. In this work, we analyze the dynamical behavior and chaos control of an atmospheric circulation model known as the Hadley circulation model, in the frame of Caputo and Caputo–Fabrizio fractional derivatives. The fundamental novelty of this paper is the application of the Caputo derivative with equal dimensionality to models that includes memory. A sliding mode controller (SMC) is developed to control chaos in this fractional-order atmospheric circulation system with uncertain dynamics. The proposed controller is applied to both commensurate and non-commensurate fractional-order systems. To demonstrate the intricacy of the models, we plot some graphs of various fractional orders with appropriate parameter values. We have observed the influence of thermal forcing on the dynamics of the system. The outcome of the analytical exercises is validated using numerical simulations.

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In this work, we analyze plankton–fish dynamics in the presence of toxicity, refuge, and combine-harvesting efforts by a considering Holling type-II functional response. We have considered phytoplankton, zooplankton, and fish populations, and the interdependent evolution is presented with the help of the Caputo fractional derivative. Since toxicity in phytoplankton spreads to zooplankton and hence to fish, we have introduced toxic terms in all the populations. On the other hand, to save the population from extinction harvesting is an essential tool. Theoretical aspects are studied in terms of nonnegativity, boundedness, existence, and uniqueness of the solution. Sufficient conditions are derived for the stability of various points of equilibrium. The composite behavior is studied by varying the values of different parameters and fractional derivatives. Numerical simulations are carried out to strengthen the theoretical findings.