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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On fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative
TL;DR: In this paper, the fractional discrete Lagrangians which differ by a fractional derivative are analyzed within Riemann-Liouville fractional derivatives, and two examples are analyzed in details.
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New applications of fractional variational principles
TL;DR: In this article, the fractional variational principles of constrained systems involving Riesz derivatives are discussed and one example is analyzed in detail, where the authors show that the Euler-Lagrange equations of two fractional Lagrangians which differ by a fractional riesz derivative are investigated.
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Fractional hamiltonian analysis of higher order derivatives systems
TL;DR: In this paper, the fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and fractional Ostrogradski's formulation is obtained, where the classical results are obtained when fractional derivatives are replaced with the integer order derivatives.
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Conservation laws and Hamilton’s equations for systems with long-range interaction and memory
TL;DR: In this article, the authors consider two different applications of the action principle: generalized Noether's theorem and Hamiltonian type equations and derive conservation laws in the form of continuity equations that consist of fractional time-space derivatives.
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Fractional-order Euler–Lagrange equations and formulation of Hamiltonian equations
TL;DR: In this article, the transversality conditions for fractional variational problems with fractional integral and fractional derivatives defined in the sense of Caputo and Riemann-Liouville are presented.
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.