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
Quantization of fractional harmonic oscillator using creation and annihilation operators
Journal ArticleDOI
Dynamical behavior of fractionalized simply supported beam: An application of fractional operators to Bernoulli-Euler theory
Journal ArticleDOI
About fractional Hamiltonian systems
TL;DR: In this paper, the authors follow Stanislavsky's approach of Hamiltonian formalism for fractional systems, as a model problem for the study of chaotic Hamiltonian systems, and prove that his formalism can be retrieved from the fractional embedding theory.
Journal ArticleDOI
Group formalism of Lie transformations, conservation laws, exact and numerical solutions of non-linear time-fractional Black–Scholes equation
TL;DR: In this article , a systematic investigation of Lie group analysis of non-linear time-fractional Black-Scholes equation including numerical approximations is presented, and conservation laws for the intended equation are derived by using a modified version of Noether's theorem.
Journal ArticleDOI
Fractional Damping Through Restricted Calculus of Variations
TL;DR: A novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping is delivered by establishing a restricted Hamilton's principle, which provides a set of numerical integrators for the continuous dynamics that are denote Fractional Variational Integrators (FVIs).
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.