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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Fractional Electromagnetic Equations Using Fractional Forms
Dumitru Baleanu,Ali Khalili Golmankhaneh,Alireza Khalili Golmankhaneh,Alireza Khalili Golmankhaneh,Mihaela Cristina Baleanu +4 more
TL;DR: In this paper, the generalized physics laws involving fractional derivatives give new models and conceptions that can be used in complex systems having memory effects using the fractional differential forms, the classical electromagnetic equations involving the fractionals derivatives have been worked out.
Journal ArticleDOI
Formulation of Hamiltonian equations for fractional variational problems
TL;DR: In this article, an extension of Riewe's fractional Hamiltonian formulation for fractional constrained systems is presented, and conditions of consistency of the set of constraints with equations of motion are investigated.
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A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials
TL;DR: In this article, the Jacobi polynomials were used to solve fractional variational problems and fractional optimal control problems (FOCPs) from the numerical point of view.
Journal ArticleDOI
Formulation of Hamiltonian Equations for Fractional Variational Problems
TL;DR: In this article, an extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems, and conditions of consistency of the set of constraints with equations of motion are investigated.
Journal ArticleDOI
About fractional quantization and fractional variational principles
TL;DR: In this article, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of a fractional generalization of the classical Faa di Bruno formula.
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.