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On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Bagley, Ron (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33In the process of constructing empirical mathematical models of physical phenomena using the fractional calculus, investigators are usually faced with the choice of which definition of the fractional derivative to use, the Riemann-Liouville definition or the Caputo definition. This investigation presents the case that, with some minimal restrictions, the two definitions produce completely equivalent mathematical models of the linear viscoelastic phenomenon....

On the extension and generation of set-valued mappings of bounded variation

V. V. Chistyakov, A. Rychlewicz (2002)

Studia Mathematica

We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...

On the fixed points in an ω -limit set

Jack G. Ceder (1992)

Mathematica Bohemica

Let M and K be closed subsets of [0,1] with K a subset of the limit points of M . Necessary and sufficient conditions are found for the existence of a continuous function f : [ 0 , 1 ] → [ 0 , 1 ] such that M is an ω -limit set for f and K is the set of fixed points of f in M .

On the Generalized Confluent Hypergeometric Function and Its Application

Virchenko, Nina (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 26A33, 33C20This paper is devoted to further development of important case of Wright’s hypergeometric function and its applications to the generalization of Γ-, B-, ψ-, ζ-, Volterra functions.

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