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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Local generalization of transversality conditions for optimal control problem
TL;DR: In this article, the transversality conditions of optimal control problems formulated with the conformable derivative were investigated and then supported by illustrative examples, and the optimal control law was achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions.
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Error analysis of spectral approximation for space-time fractional optimal control problems with control and state constraints
TL;DR: In this paper , the spectral discretization of optimal control problem governed by the space-time fractional diffusion equation with integral control and state constraints is investigated, and the analysis results indicate that the errors decay exponentially when the data is smooth.
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Linear non-conservative systems with fractional damping and the derivatives of critical load parameter
TL;DR: In this article, the influence of small perturbation on a linear, non-conservative dynamical system exhibiting a flutter type bifurcation has been investigated, and a new analytical framework for the optimization of aero-structural systems, exhibiting the non-classical damping is presented.
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Fractional variational problems depending on fractional derivatives of differentiable functions with application to nonlinear chaotic systems
TL;DR: In this article, a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum was formulated and the Euler-Lagrange equation was obtained.
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A fractional optimal control problem with final observation governed by wave equation.
TL;DR: In this paper, the problem of controlling the source function for an optimal control problem involving the fractional wave equation was considered and an optimal solution was derived for the considered fractional optimal control problems.
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.