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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A fast numerical method for solving calculus of variation problems
TL;DR: In this article, the authors used the differential transform method (DTM) for solving some problems in calculus of variations (COPD) and showed the efficiency of the proposed technique.
Journal ArticleDOI
Fractional variational principles and their applications
TL;DR: In this paper, a fractional Lagrangian and Hamiltonian formalism is presented within the Riemann-Liouville fractional derivatives and the anharmonic oscillator is analyzed.
Journal ArticleDOI
Analytical study of D-dimensional fractional Klein–Gordon equation with a fractional vector plus a scalar potential
TL;DR: In this article, a fractional Klein-Gordon equation with fractional vector and scalar potential has been studied, where both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely v and s. This manipulation delivers fractional-type confluent hypergeometric equation to solve.
Numerical solution of fractional euler-lagrange equation with multipoint boundary conditions
TL;DR: In this article, the authors considered an ordinary fractional differential equation containing a composition of left and right fractional derivati vees and proposed a numerical scheme using the finite difference method.
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On exact solutions of a class of fractional Euler-Lagrange equations
Dumitru Baleanu,Juan J. Trujillo +1 more
TL;DR: In this article, a class of fractional differential equations are obtained by using the fractional variational principles, and exact solutions for some Euler-Lagrange equations are presented, in particular for the following equations.
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.