he major goal of the this work is to present an optimal design of the Fractional-order Proportional-Derivative-Integral (FoPID) controller for the single-joint arm dynamics. For meeting this aim, the Particle Swarm Optimization (PSO) algorithm will be implement to tune the parameters of such controller. Six FoPID-controllers will be generated in accordance with two kinds of approaches (Continued Fraction Expansion (CFE) and Outstaloup’s approaches) for Laplacian operators, coupled with three fitness functions (IAE, ITAE, ITSE). These controllers will be competed to each other to determine which one can provide to the closed-loop system of the single-joint robot arm model a good rise time, short settling time, and an excellent overshoot. Keywords: Fractional-order model; Oustaloup approximation, Continued
Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. A new theorem is proven which highlights that the pandemic disappears when an inequality involving the percentage of the population in quarantine is satisfied. Finally, numerical simulations are carried out to show that the proposed incommensurate fractional-order model is effective in describing the spread of the COVID-19 pandemic.
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