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Fractional-order system. In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. [1] Such systems are said to have fractional dynamics. Derivatives and integrals of fractional orders are used to ...
Fractional-order control. Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods and strategies. [1]
Fractional calculus was introduced in one of Niels Henrik Abel's early papers [3] where all the elements can be found: the idea of fractional-order integration and differentiation, the mutually inverse relationship between them, the understanding that fractional-order differentiation and integration can be considered as the same generalized ...
Miscellanea. v. t. e. A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative (usually called a differintegral) of an input. Differentiation or integration is a real or complex parameter. The fractional integrator is useful in fractional-order control ...
The Fractional calculus of sets, first introduced in the article titled "Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods", [1] is a methodology derived from fractional calculus. [2]
The fractional Chebyshev collocation (FCC) method[1] is an efficient spectral method for solving a system of linear fractional-order differential equations (FDEs) with discrete delays. The FCC method overcomes several limitations of current numerical methods for solving linear FDEs. For instance, the FCC method can be used for linear ...
First-order means that only the first derivative of y appears in the equation, and higher derivatives are absent. Without loss of generality to higher-order systems, we restrict ourselves to first-order differential equations, because a higher-order ODE can be converted into a larger system of first-order equations by introducing extra variables.
Multi-fractional order estimator. In target tracking, the multi-fractional order estimator (MFOE) [1][2] is an alternative to the Kalman filter. [3][4][5] The MFOE is focused strictly on simple and pragmatic fundamentals along with the integrity of mathematical modeling. Like the KF, the MFOE is based on the least squares method (LSM) invented ...