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
More filters
Journal ArticleDOI
Hamiltonian formulation of classical fields with fractional derivatives: revisited
TL;DR: In this article, an investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation, and the resulting equations are very similar to those appearing in classical field theory.
Journal ArticleDOI
Necessary Conditions to A Fractional Variational Problem
TL;DR: In this article , the authors make a comparison between the Euler-Lagrange equation and the Riemann-Liouville equation for solving a particular fractional variational problem and obtain some conclusions about the optimal solution.
Journal ArticleDOI
Fractional model of blood flow and rogue waves in arterial vessels
TL;DR: In this paper , a new mathematical model has been proposed to describe rogue waves in arterial vessels based on two-dimensional Navier-Stokes (NS) equation and continuity equation, vorticity equation satisfied by blood flow is given.
Journal ArticleDOI
On Fractional Dynamics on the Extended Phase Space
Dumitru Baleanu,Sami I. Muslih,Eqab M. Rabei,Alireza Khalili Golmankhaneh,Ali Khalili Golmankhaneh +4 more
TL;DR: In this article, the fractional Hamiltonian on the extended phase space is analyzed and the corresponding generalized Poisson's brackets are constructed, and a fractional calculus should be applied to various dynamical systems in order to validate in practice.
Existence of positive solutions for fractional differential equations with Riemann-Liouville left-hand and right-hand fractional derivatives
TL;DR: In this article, the authors combine properties of Riemann-Liouville fractional calculus and fixed point theorems to obtain three existence results of one positive solution and of multiple positive solutions for initial value problems with fractional dierential equations.
References
More filters
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.