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
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Fractional Noether's Theorem with Classical and Caputo Derivatives: constants of motion for non-conservative systems
TL;DR: In this paper, a generalization of the Noether's theorem for Lagrangians depending on mixed classical and Caputo derivatives is presented, which can be used to obtain constants of motion for dissipative systems.
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Fractional optimal control problem for variable-order differential systems
TL;DR: In this paper, the authors apply the classical control theory to a variable order fractional differential system in a bounded domain and show that the considered optimal control problem has a unique solution, where the performance index is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) with variable order.
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Models and Numerical Solutions of Generalized Oscillator Equations
Yufeng Xu,Om P. Agrawal +1 more
TL;DR: In this article, the generalized harmonic oscillators are defined using a generalized Euler-Lagrange equation and a finite difference scheme is presented to solve these equations in closed form.
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Isoperimetric problems of the calculus of variations with fractional derivatives
TL;DR: In this article, the authors studied isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives and considered both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bounds of the fractional derivative.
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An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems
Neelam Singha,Chandal Nahak +1 more
TL;DR: A class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives, is discussed, and the necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions.
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.