Wyniki wyszukiwania - BazTech

1

A generalized fractional calculus of variations

Odzijewicz T., Malinowska A. B., Torres D. F. M.

Control and Cybernetics

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2013

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Vol. 42, no. 2

443--458

EN

We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, transversality conditions for free boundary value problems, and a generalized Noether type theorem.

2

On reflection symmetry in fractional mechanics

Klimek M., Lupa M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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Vol. 10, nr 1

109-121

EN

We study the properties of fractional differentiation with respect to reflection mapping in a finite interval. The symmetric and anti-symmetric fractional derivatives in a full interval are expressed as fractional differential operators in left or right subintervals obtained by subsequent partitions. These representation properties and the reflection symmetry of the action and variation are applied to derive Euler-Lagrange equations of fractional free motion. Then the localization phenomenon for these equations is discussed.

3

Fractional Euler-Lagrange equations : numerical solutions and applications of reflection operator

Błaszczyk T., Ciesielski M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2010

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Vol. 9, nr 2

17-24

EN

In this work numerical solutions of fractional Euler-Lagrange equations describing free motion are considered. This type of equations contains a composition of left and right fractional derivatives. A reflection operator is applied to obtain relations between the Euler-Lagrange equations. In addition we verify the dependence between the respective numerical schemes using the same operator. In the final part of paper the examples of the numerical solutions are shown.

4

The delta-nabla calculus of variations

Malinowska A. B., Torres D. F. M.

Fasciculi Mathematici

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2010

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Nr 44

75-83

EN

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.

5

Theoretical foundations of a Dynamic Inertial Bumper (DIB) design

Dobry M. W.

Vibrations in Physical Systems

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2006

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Vol. 22

107--112

6

Stability of the Euler-Lagrange-Rassias functional equation

Pietrzyk A.

Demonstratio Mathematica

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2006

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Vol. 39, nr 3

523-530

EN

Let F be a field, a1, a2 is an element of F, K is an element of {R, C}, s an element of K\{0,1}, X be a linear space over F, S C is contained in X be nonempty, and Y be a Banach space over K. Under some additional assumptions on S we show some stability results for the functional equation Q (a1x + a2y) + Q (a2X - a1y) = s[Q{x) + Q{y)} in the class of function Q : S -> Y.

7

Field of complex linear frames on real space-time manifold as dynamical variable for generally-covariant models

Godlewski P.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

819--835

EN

A model of the self-interacting field of complex linear frames E on an n-dimensional real manifold is investigated. The model is generally-covariant and GL(n, C)- invariant. If n = 4, the components of E can be interpreted as dynamical variables for the gravitational field. A Lagrangian of E is constructed, the Euler-Lagrange equations are derived and a wide class of their solutions is found. The solutions are built of left invariant vector fields on a real semisimple Lie group "deformed" by a complex factor of a natural exponential structure.