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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The Dual Action of Fractional Multi Time Hamilton Equations
Dumitru Baleanu,Ali Khalili Golmankhaneh,Alireza Khalili Golmankhaneh,Alireza Khalili Golmankhaneh +3 more
TL;DR: In this article, the fractional multi-time Lagrangian equations for dynamical systems within Riemann-Liouville derivatives were derived and the corresponding fractional Euler-Lagrange and Hamilton equations were obtained.
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Fractional optimal control problem for differential system with control constraints
TL;DR: In this paper, the fractional optimal control problem for differential systems is considered in a Riemann-Liouville sense, and necessary and sufficient optimality conditions for fractional Dirichlet and Neumann problems with quadratic performance functional are derived.
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Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems
Ali Lotfi,Sohrab Ali Yousefi +1 more
TL;DR: Epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems and the choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed.
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Fedosov Quantization of Fractional Lagrange Spaces
Dumitru Baleanu,Sergiu I. Vacaru +1 more
TL;DR: In this article, a nonholonomic deformation (Fedosov type) quantization of fractional Lagrange-Finsler geometries has been performed for a fractional almost Kahler model encoding equivalently all data for fractional Euler-Lagrange equations with Caputo fractional derivative.
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Conservation laws, soliton-like and stability analysis for the time fractional dispersive long-wave equation
TL;DR: In this paper, the conservation laws with Riemann-Liouville (RL) for the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE are derived.
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.