Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review

By YangQuan Chen, Blas M. Vinagre, Igor Podlubny. 2004

339 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1a68fac863686c9a8ceacd88936b1c656ecb157c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

An improved non-classical method for the solution of fractional differential equations (2010, background): “Moreover, the design of fractional circuits and systems, including fractional control, have received strong attention [3, 11 ,12,19,31].”
On the biquadratic approximation of fractional-order Laplacian operators (2013, methodology): “Several methods have been developed to approximate the fractional-order operators (whether fractional-order differentiators or integrators) by finite-order transfer functions [1,2,3,13,14].”
Galerkin Projections and Finite Elements for Fractional Order Derivatives (2006, background): “Other finite dimensional approximations, as in [10, 11], will give similar time savings.”
UBIQUITOUS FRACTIONAL ORDER CONTROLS (2006, methodology): “For controller tuning techniques, refer to (Monje et al., 2004; Chen et al., 2004a).”
Stability analysis of Caputo fractional-order nonlinear systems revisited (2011, background): “In recent years, numerous studies and applications of fractionalorder systems in many areas of science and engineering have been presented [1–11].”
Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems (2008, positive): “Al-Alaoui operator is a credible alternative to other discretization methods with wide range of applications in integer and fractional order discretization and other applications that require accurate and real time differentiation or integration [15–44].”
Fractional variational optimal control problems with delayed arguments (2010, methodology): “In control theory the fractional calculus was used by several authors, and interesting results were reported [15–19].”
Adaptive backstepping output feedback control for a class of nonlinear fractional order systems (2016, background): “For the details of the most recent advance, one can refer to some excellent monographs [3–5] survey papers [6,7], and the references listed in them.”