Abstract
Fractional-order Geomagnetic Field model is considered in this work. A sufficient condition is used to prove that the solution of the fractional-order Geomagnetic Field model exists and is unique in a specific region. Conditions for continuous dependence on initial conditions in our model are discussed. In addition, the conditions of local stability of the model's five equilibrium points are obtained. Chaotic attractors are shown to exist in the proposed fractional model. Also, Lyapunov exponents of the fractional-order Geomagnetic Field model are calculated and computations of Lyapunov spectrum as functions of all the model's parameters and fractional-order are performed. Moreover, a novel linear control technique based on Lyapunov stability theory is introduced here to stabilize the chaotic states of the fractional-order Geomagnetic Field model to its five equilibrium points. Finally, to verify the validity of our theoretical results and the effectiveness of the control scheme, numerical simulations based on the Atangana–Baleanu fractional integral in Caputo-sense are done to produce the chaotic attractors.