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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Book ChapterDOI
Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives
G. M. Bahaa,A. Atangana +1 more
TL;DR: In this paper, the necessary and sufficient optimality conditions for systems involving Atangana-Baleanu derivatives are discussed, and a general formulation and a solution scheme for a class of Fractional Optimal Control Problems (FOCPs) for those systems are presented.
Journal ArticleDOI
Optimal charging of fractional-order circuits with Cuckoo search.
Amr M. AbdelAty,Mohammed E. Fouda,Mohammed E. Fouda,Menna T. M. M. Elbarawy,Ahmed G. Radwan,Ahmed G. Radwan +5 more
TL;DR: In this article, the authors used a meta-heuristic optimization technique called Cuckoo search optimizer to attain the maximum charging efficiency of three common fractional-order RC circuits.
An application of the Rayleigh-Ritz method for solving fractional oscillator equation
TL;DR: Blaszczyk et al. as mentioned in this paper proposed a scheme based on the variational Rayleigh-Ritz method to obtain a numerical solution of the fractional oscillator equation, which is a type of equation which includes a composition of left and right fractional derivatives.
Journal ArticleDOI
Adiabatic Invariants for Generalized Fractional Birkhoffian Mechanics and Their Applications
TL;DR: Perturbation to Noether symmetry and adiabatic invariants for the generalized fractional Birkhoffian system with the combined Riemann-Liouville fractional derivatives and the combined Caputo fractional derivative, respectively, are investigated in this paper.
Journal ArticleDOI
Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas
TL;DR: In this article, a construction of fractional differential geometry of curves (curvature of curve and Frenet-Serret formulas) is discussed, where a tangent vector of plane curve is defined by the Caputo fractional derivative.
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.