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In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance is commonly used in engineering, chemistry, and medicine to study complex materials by relating magnetization to applied radiofrequency, gradient, and static magnetic fields through the Bloch equation. Chaos in the Bloch equation is a key factor in many important applications. This study focuses on the study of the Bloch equation under the influence of the Caputo fractional derivative, both with and without delay, and explores the underlying chaos using a sliding mode controller. The controller's effectiveness is observed under uncertainty and external disturbances for both commensurate and incommensurate systems, and theoretical aspects such as the existence and uniqueness of solutions and the stability of the controlled system are examined. Lyapunov exponents are calculated for various fractional derivatives to demonstrate the presence of chaos in the system, and numerical simulations are used to verify theoretical assertions. [ABSTRACT FROM AUTHOR]