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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Journal ArticleDOI
Variational integrator for fractional Euler–Lagrange equations
TL;DR: In this article, the notion of variational integrator for classical Euler-Lagrange equations was extended to the fractional case and it was shown that variational integration allows to preserve Noether-type results at the discrete level.
On the fractional-order diffusion-wave process
TL;DR: A.E.HERZALLAH, AHMEDI M.A. EL-SAYED, DUMITRU BALEANU Faculty of Science at Zagazig University, Zagazi, Egypt.
Proceedings ArticleDOI
Implantable Pacemakers Control and Optimization via Fractional Calculus Approaches: A Cyber-Physical Systems Perspective
TL;DR: A fractal approach to pacemaker design is introduced by modeling the heart rate dynamics via fractional differential equations and it is shown that the constrained finite horizon optimal control problem can be reduced to solving a linear system.
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Fractional Dynamics of Relativistic Particle
TL;DR: In this article, the relativistic invariance of a particle subjected to a non-potential four-force is considered as a nonholonomic system. And conditions for the fractional dynamics of the particle to be a Hamiltonian system are considered.
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Optimal control of variable-order fractional model for delay cancer treatments
TL;DR: The fractional model is used to test the hypothesis that a combination of anti-Vascular Endothelial Growth Factor treatment with immunotherapy, involving injections of unlicensed dendritic cells (DC), can lead to the tumor eradication by concealing the suppressor VEGF.
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.