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Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Krishna, B., Reddy, K. (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 93B51, 93C95In this paper, design of fractional order digital differentiators and integrators using indirect discretization is presented. The proposed approach is based on using continued fraction expansion to find the rational approximation of the fractional order operator, s^α. The rational approximation thus obtained is discretized by using s to z transforms. The proposed approach is tested for differentiators and integrators of orders 1/4 and 1/2. The...

Design of unknown input fractional-order observers for fractional-order systems

Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)

International Journal of Applied Mathematics and Computer Science

This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the...

Discrete Models of Time-Fractional Diffusion in a Potential Well

Gorenflo, R., Abdel-Rehim, E. (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity...

Distributional fractional powers of the Laplacean. Riesz potentials

Celso Martínez, Miguel Sanzi, Francisco Periago (1999)

Studia Mathematica

For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, ( ( - Δ ) α u , ϕ ) = ( u , ( - Δ ) α ϕ ) , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...

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