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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Book ChapterDOI
A Fractional Calculus Application to Biological Reactive Systems
Vicente Rico-Ramirez,Jesus Martinez-Lizardo,Gustavo A. Iglesias-Silva,Salvador Hernández-Castro,Urmila M. Diwekar +4 more
TL;DR: In this article, it was shown that the dynamics of some reactive systems displaying atypical behavior can be represented by fractional order differential equations (FDE), and when the resulting dynamic system is incorporated into an optimization framework to achieve optimal performance, the resulting problem is a fractional optimal control problem (FOCP).
Journal ArticleDOI
Formalization of Euler–Lagrange Equation Set Based on Variational Calculus in HOL Light
TL;DR: The fundamental lemma of variational calculus is formally verified, some basic concepts such as functional variation and the necessary conditions for functional extreme are formalized, and the Euler–Lagrange equation set is formalized.
Journal ArticleDOI
Variational methods for fractional q-Sturm-Liouville problems
TL;DR: In this article, a regular q-fractional Sturm-Liouville problem (qFSLP) is formulated and the existence of a countable set of real eigenvalues and associated orthogonal eigenfunctions is proved.
Posted Content
Effect of the fluctuations around mean field for N-body systems with long range interactions
Y. Chaffi,R. Casta,L. Brenig +2 more
TL;DR: In this article, the effect of Chandrasekhar and Holstmark's distribution of field fluctuations on the dynamics of N-body systems interacting via Coulomb or Newton gravitational force was studied.
Journal ArticleDOI
Euler–Lagrange equations for variational problems involving the Riesz–Hilfer fractional derivative
Ahmed Ibrahim,A. A. Elmandouh +1 more
TL;DR: In this article, the Euler-Lagrange equations for different kinds of variational problems with the Lagrangian function containing the Riesz-Hilfer fractional derivative were obtained.
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.