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 General Formulation and Solution Scheme for Fractional Optimal Control Problems
TL;DR: In this article, a general formulation and a solution scheme for a class of Fractional Optimal Control Problems (FOCPs) for those systems are presented, where the performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of FDEs.
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Fractional variational calculus in terms of Riesz fractional derivatives
TL;DR: In this article, the transversality conditions for fractional variational problems (FVPs) defined in terms of Riesz fractional derivatives (RFDs) are considered.
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Modeling with fractional difference equations
Ferhan M. Atıcı,Sevgi Şengül +1 more
TL;DR: In this paper, the authors developed some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula and derived Euler-Lagrange equation.
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A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
Om P. Agrawal,Dumitru Baleanu +1 more
TL;DR: In this paper, the Riemann-Liouville Fractional Derivatives (RLFDs) were used to solve fractional optimal control problems (FOCPs).
References
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Book
Energy and variational methods in applied mechanics : with an introduction to the finite element method
TL;DR: A review of the equations of MECHANICS can be found in this paper, where the Ritz Method and Weighted-Residual Methods are used to approximate the distance between two points.
Book
Calculus of variations : with applications to physics and engineering.
TL;DR: This is likewise one of the factors by obtaining the soft documents of this calculus of variations with applications to physics and engineering by online as discussed by the authors. But it will agreed squander the time.