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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Proceedings ArticleDOI
Fractional Euler-Lagrange Equations for Constrained Systems
Tansel Avkar,Dumitru Baleanu +1 more
TL;DR: In this paper, the Euler-Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus, which generalizes the notions of n−fold integration and integer-order differentiation.
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Generalized fractional hybrid Hamilton Pontryagin equations
Chis Oana,Opris Dumitru +1 more
TL;DR: In this article, the generalized fractional hybrid process was introduced and generalized fraction fractional Langevin process was used to find the Langevin Langevin equation and numerical simulations were done.
Journal ArticleDOI
Path Integral Quantization of Singular Lagrangians using Fractional Derivatives
TL;DR: In this article, a general theory for quantizing singular systems within the framework of fractional calculus using the path integral approach is given, and the fractional singular Lagrangians and fractional path integral representation are presented.
Journal ArticleDOI
Fractional cyber-neural systems — A brief survey
TL;DR: In this article , the authors provide an overview of fractional cyber-neural systems (CNS) that entail fractional-order systems in the context of CNS, including system identification, state estimation, and closed-loop control.
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Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives
TL;DR: In this article, a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects is studied.
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.