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
Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation
TL;DR: The dynamics of the simple pendulum is presented by using the fractional-order derivatives to perform equilibria analysis and indicate the conditions where stability dynamics can be observed for both integer and fractional order models.
Journal ArticleDOI
Noether-type theorem for fractional variational problems depending on fractional derivatives of functions
TL;DR: In this paper, a generalized fractional calculus of variation was proposed, where the Lagrangian function depends on fractional derivatives of differentiable functions, and the Euler-Lagrange equation generalizes previously results and enables us to construct simple Lagrangians for nonlinear systems.
Journal ArticleDOI
On the motion of a heavy bead sliding on a rotating wire - Fractional treatment
TL;DR: In this article, the authors considered the motion of a heavy particle sliding on a rotating wire and derived the fractional Hamilton's equations (FHEs) of motion of the system is derived.
Posted Content
Stochastic Fractional HP Equations
Chis Oana,Opris Dumitru +1 more
TL;DR: In this article, the condition for a curve to satisfy stochas-tic fractional HP (Hamilton-Pontryagin) equations was established, and Langevin fractional equations were found and numerical simulations were done.
Journal ArticleDOI
Existence of solutions for Kirchhoff-type fractional Dirichlet problem with $p$-Laplacian
TL;DR: In this article, the authors investigated the existence of solutions for a class of p-Laplacian fractional order Kirchhoff-type systems with Riemann-Liouville fractional derivatives and a parameter λ.
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.