Displaying similar documents to “An application of fractional calculus”

Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Tadeusz Kaczorek, Krzysztof Rogowski (2010)

International Journal of Applied Mathematics and Computer Science

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A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure...

Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.

Chu Wenchang (1997)

Collectanea Mathematica

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A pair of simple bivariate inverse series relations are used by embedding machinery to produce several double summation formulae on shifted factorials (or binomial coefficients), including the evaluation due to Blodgett-Gessel. Their q-analogues are established in the second section. Some generalized convolutions are presented through formal power series manipulation.