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
Citations
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Fractional Pais–Uhlenbeck Oscillator
TL;DR: In this paper, the fractional Lagrangian of Pais-Uhlenbeck oscillator was studied numerically based on the Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference).
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Fractional generalized Hamiltonian equations and its integral invariants
Shao-Kai Luo,Lin Li +1 more
TL;DR: In this paper, a new kind of fractional dynamical equations, i.e., the fractional generalized Hamiltonian equations, and the method of the construction of integral invariants of the system are established.
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Comparative study for optimal control nonlinear variable-order fractional tumor model
TL;DR: In this article, a variable order nonlinear mathematical model and its optimal control for a Tumor under immune suppression was presented, which adopts a variable-order fractional model with the derivatives defined in the Caputo sense.
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Fractional Bateman-Feshbach Tikochinsky Oscillator
TL;DR: In this paper, the fractional Lagrangian and Hamiltonian of the complex Bateman-Feshbach Tikochinsky oscillator were analyzed using the Grunwald-Letnikov approach.
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Fractional Constrained Systems and Caputo Derivatives
TL;DR: In this article, the fractional dynamics of discrete constrained systems is presented and the notion of reduced phase space is discussed, where the variational principles have been used in physics to construct the phase space of a fractional dynamical system.
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.