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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4.0. Remarks on fractional Hamiltonian formulation of discrete systems with
Noorhan Alshaikh,Jihad H. Asad +1 more
TL;DR: In this article , the Fractional Hamiltonian is used to investigate discrete systems in terms of Caputo's fractional derivatives, and three models have been introduced and studied in order to apply the formalism presented here.
Proceedings ArticleDOI
Modes of Asymmetrical Anchoring Slab Liquid Crystal Optical Waveguide
TL;DR: In this paper , the authors derived the dispersion relation of transverse magnetic mode in asymmetrical anchoring slab liquid crystal optical waveguide under the condition of gradual change of liquid crystal director.
Optimality conditions involving the Mittag–Leffler tempered fractional derivative
Ricardo Almeida,M. Luísa Morgado +1 more
TL;DR: In this article, a numerical method is presented, based on discretization of the variational problem, for solving problems of the calculus of the variations, where the differential operator is a generalisation of the tempered fractional derivative.
Journal ArticleDOI
A reliable numerical approach for analyzing fractional variational problems with subsidiary conditions
TL;DR: In this article, the authors obtain the necessary optimality conditions for a new class of isoperimetric fractional variational problems depending on indefinite integrals (IFVPDI), and a modified direct numerical approach based on the Epsilon-Ritz method and polynomial basis functions is applied.
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.