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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Proceedings ArticleDOI
Modes of Asymmetrical Anchoring Slab Liquid Crystal Optical Waveguide
Zhengtao Zha,Qianshu Zhang +1 more
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.
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Dynamical modeling and physical analysis of pipe flow in hydraulic systems based on fractional variational theory
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Novel analytical technique to find diversity of solitary wave solutions for Wazwaz-Benjamin-Bona Mahony equations of fractional order
TL;DR: In this article , the newly modified Benjamin-Bona-Mahony equations in three dimensions are examined in the current work through the use of conformable fractional derivatives to incorporate spatial and temporal fractional order derivatives.
Journal ArticleDOI
Variational problems of variable fractional order involving arbitrary kernels
TL;DR: In this article , the Euler-Lagrange equation is defined as a necessary condition that every optimal solution of the problem must satisfy, and the Herglotz variational problem is studied with integral and holonomic constraints.
Towards a combined fractional mechanics
TL;DR: In this article, a fractional Hamiltonian formalism is introduced for the recent com-bined fractional calculus of variations, which provides tools to carry out the quantization of non-conservative problems through combined fractional canonical equations of Hamilton type.
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.