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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Time-fractional electron-acoustic shocks in magnetoplasma with superthermal electrons
TL;DR: In this paper , the linear and nonlinear characteristics of electron-acoustic (EA) shocks are examined in an electron-ion (EI) magnetoplasma containing superthermal electrons.
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Fractional euler-lagrange and fractional hamilton equations for super symmetric classical model
Dumitru Baleanu,Sami I. Muslih +1 more
TL;DR: In this paper, the super fractional Hessian was defined and the fractional Hamiltonian of the super symmetric classical model was constructed in the presence of the elements of Berezin algebra.
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Lagrangian formulation of Born-Infeld electrodynamics in fractional space
TL;DR: In this paper, a fractional generalization of the Born-Infeld electrodynamics in vector form is found and corresponding to fractal Born-infeld equations, the Laplace and Poisson equations in fractional space are derived.
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Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives
TL;DR: In this paper , a generalized proportional fractional derivative is proposed for variational problems, where ordinary derivatives are replaced by a generalized proportionality operator, acting as a weight over the state function and its first-order derivative.
Método Numérico de Tipo L1 para Problemas Variacionales Fraccionarios
TL;DR: In this article, a nuevo metodo numerico basado en el metodo L1 was presented to obtener aproximaciones a las soluciones of this tipo de problemas.
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.