7,027 research outputs found
A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
We introduce a fractional theory of the calculus of variations for multiple
integrals. Our approach uses the recent notions of Riemann-Liouville fractional
derivatives and integrals in the sense of Jumarie. Main results provide
fractional versions of the theorems of Green and Gauss, fractional
Euler-Lagrange equations, and fractional natural boundary conditions. As an
application we discuss the fractional equation of motion of a vibrating string.Comment: Accepted for publication in the Journal of Mathematical Physics
(14/January/2010
Fractional Noether's theorem in the Riesz-Caputo sense
We prove a Noether's theorem for fractional variational problems with
Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are
obtained. Illustrative examples in the fractional context of the calculus of
variations and optimal control are given.Comment: Accepted (25/Jan/2010) for publication in Applied Mathematics and
Computatio
A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
This paper presents the Euler-Lagrange equations for fractional variational
problems with multiple integrals. The fractional Noether-type theorem for
conservative and nonconservative generalized physical systems is proved. Our
approach uses well-known notion of the Riemann-Liouville fractional derivative.Comment: Submitted 26-SEP-2011; accepted 3-MAR-2012; for publication in
Applied Mathematics Letter
Fractional Calculus of Variations for Double Integrals
We consider fractional isoperimetric problems of calculus of variations with
double integrals via the recent modified Riemann-Liouville approach. A
necessary optimality condition of Euler-Lagrange type, in the form of a
multitime fractional PDE, is proved, as well as a sufficient condition and
fractional natural boundary conditions.Comment: Submitted 07-Sept-2010; revised 25-Nov-2010; accepted 07-Feb-2011;
for publication in Balkan Journal of Geometers and Its Applications (BJGA
Calculus of variations with fractional derivatives and fractional integrals
We prove Euler-Lagrange fractional equations and sufficient optimality
conditions for problems of the calculus of variations with functionals
containing both fractional derivatives and fractional integrals in the sense of
Riemann-Liouville.Comment: Accepted (July 6, 2009) for publication in Applied Mathematics
Letter
Fractional variational problems with the Riesz-Caputo derivative
In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. © 2011 Elsevier Ltd. All rights reserved.FCTCIDM
Variable Order Fractional Variational Calculus for Double Integrals
We introduce three types of partial fractional operators of variable order.
An integration by parts formula for partial fractional integrals of variable
order and an extension of Green's theorem are proved. These results allow us to
obtain a fractional Euler-Lagrange necessary optimality condition for variable
order two-dimensional fractional variational problems.Comment: This is a preprint of a paper whose final and definite form will be
published in: 51st IEEE Conference on Decision and Control, December 10-13,
2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1240.d4462b33.
Submitted 07-March-2012; accepted 17-July-201
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