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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Fractional ordered Liu system with time-delay
TL;DR: In this article, the effect of delay on the chaotic behavior of fractional ordered Liu systems has been investigated for the first time in the literature and it has been demonstrated that the chaotic systems can be transformed into limit cycles or stable orbits with appropriate choice of delay parameter.
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New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator
TL;DR: In this article, the free motion of a fractional capacitor microphone is investigated and the Euler-Lagrange equations are established, and numerical simulations are obtained and dynamical behaviors are numerically discussed.
Journal ArticleDOI
A new and general fractional Lagrangian approach: A capacitor microphone case study
Amin Jajarmi,Dumitru Baleanu,Dumitru Baleanu,K. Zarghami Vahid,H. Mohammadi Pirouz,Jihad H. Asad +5 more
TL;DR: In this paper, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system, where the classical Euler-Lagrange equations are constructed by using the classical Lagrangian approach.
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A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations
TL;DR: In this article, a fractional extension of a mass-conserving Allen-Cahn phase field model was developed to control the sharpness of the interface, which is typically diffusive in integer-order phase field models.
Journal Article
Computational methods in the fractional calculus of variations and optimal control
TL;DR: In this paper, the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences is investigated, and upper bounds for the error of proposed approximations and study their efficiency.
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.