Formulation of Euler–Lagrange equations for fractional variational problems
TLDR
In this article, the Euler-Lagrange type necessary conditions which must be satisfied for the given functional to be extremum were developed for systems containing fractional derivatives, where the fractional derivative is described in the Riemann-Liouville sense.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2002-08-01 and is currently open access. It has received 866 citations till now. The article focuses on the topics: Fractional calculus & Euler–Lagrange equation.read more
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Fractional fundamental lemma and fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems
Loïc Bourdin,Dariusz Idczak +1 more
TL;DR: In this paper, a fractional integral representation of functions possessing Riemann-Liouville fractional derivatives is derived, based on the integral representation derived in this paper too.
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Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
Dumitru Baleanu,Sergiu I. Vacaru +1 more
TL;DR: In this article, methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics.
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Fractional optimal control problem for differential system with delay argument
TL;DR: In this article, the authors apply the classical control theory to a fractional differential system in a bounded domain, and consider the fractional optimal control problem (FOCP) for differential system with time delay.
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Optimality conditions for fractional differential inclusions with nonsingular Mittag–Leffler kernel
TL;DR: In this paper, a differential inclusions problem with fractional-time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces is considered and the existence and uniqueness of solution are proved by means of the Dubovitskii-Milyutin theorem.
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Fractional Almost Kahler - Lagrange Geometry
Dumitru Baleanu,Sergiu I. Vacaru +1 more
TL;DR: In this article, the fractional Lagrange dynamics are encoded as a nonholonomic almost Kahler geometry, which is a generalization of the Finsler Lagrange generating function.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
BookDOI
Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.