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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Design and Implementation of Optical Flow Estimator for Moving Object Detection in Advanced Driver Assistance System
TL;DR: In the proposed design, Brox's algorithm with global optimization is considered, which shows the high performance in the vehicle environment, and Cholesky factorization is applied to solve Euler-Lagrange equation in BroX's algorithm.
Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties
TL;DR: The generalized Clifford algebra as mentioned in this paper is a generalization of Dirac's factorization of the d'Alembert operator to higher order forms, and it can be used to obtain a fractional partial differential matrix equation.
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Numerical approximation of fractional variational problems with several dependent variables using Jacobi poly-fractonomials
TL;DR: In this article , a new numerical scheme using Jacobi poly-fractonomials for the fractional variational problem (FVP) with several dependent variables is discussed. And the convergence of the presented scheme and the FVP error is proved.
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Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels
TL;DR: In this paper, the authors considered Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function and proved necessary optimality conditions for the Herglots fractional variational problem with and without time delay.
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The new formulation of Hamiltonian second order continuous systems of Riemann-Liouville fractional derivatives
Y. Alawaideh,B. M. Alkhamiseh +1 more
TL;DR: In this article , the authors generalized the Hamilton formulation for continuous systems with second-order fractional derivatives and applied it to Podolsky's generalized electrodynamics, and compared the outcomes to those obtained using Dirac's approach.
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.