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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Book ChapterDOI
Fractional Nonholonomic Dynamics
TL;DR: In this paper, the fractional nonholonomic constraints are interpreted as constraints with long-term memory with power-law longterm memory by using fractional derivatives of non-integer orders.
Proceedings ArticleDOI
Nontrivial Solutions of Singular Sign-Changing Nonlinear Dirichlet-Type Fractional Differential Equation
TL;DR: In this article, the Leray-Schauder degree was established for a class of singular sign-changing nonlinear Dirichlet-type fractional differential equations for continuous fields.
Journal ArticleDOI
New Variational Problems with an Action Depending on Generalized Fractional Derivatives, the Free Endpoint Conditions, and a Real Parameter
Ricardo Almeida,Natália Martins +1 more
TL;DR: Conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders are proved.
Journal ArticleDOI
Numerical solution of fractional variational and optimal control problems via fractional-order Chelyshkov functions
TL;DR: In this article , a new numerical method based on the fractional-order Chelyshkov functions (FCHFs) for solving fractional variational problems and fractional optimal control problems is presented.
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.