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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Variational principle of stationary action for fractional nonlocal media and fields
TL;DR: In this paper, an extension of the standard variational principle for fractional nonlocal media with power-law type nonlocality is described by the Riesz-type derivatives of non-integer orders.
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Space-Time Fractional DKP Equation and Its Solution
N. Bouzid,M. Merad +1 more
TL;DR: In this paper, a fractional Hamiltonian formulation for DKP fields is presented and, as done in the framework of the Lagrangian formalism, the fractional DKP equation is deduced.
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An Exact Solution of the Second-Order Differential Equation with the Fractional/Generalised Boundary Conditions
TL;DR: In this article, the initial/boundary value problem for the second-order homogeneous differential equation with constant coefficients was analyzed and particular solutions to the considered problem were presented, and illustrative examples are shown.
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On the Existence and Continuous Dependence on Parameter of Solutions to Some Fractional Dirichlet Problem with Application to Lagrange Optimal Control Problem
Rafał Kamocki,Marek Majewski +1 more
TL;DR: In the paper, a Lagrange optimal control problem governed by a fractional Dirichlet problem with the Riemann–Liouville derivative is considered and continuous dependence is applied to show the existence of optimal solution to the Lagrange problem.
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Erratum: "complexified fractional heat kernel and physics beyond the spectral triplet action in non-commutative geometry"
TL;DR: In this article, the fractional spectral triplet action is complexified and the disturbing huge cosmological term may be eliminated, and the generalization of the problem in view of the generalized fractional integration operators, namely the Erdelyi-Kober fractional integral is also discussed.
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.