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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Ground state solution for differential equations with left and right fractional derivatives
TL;DR: In this paper, the mountain pass theorem and comparison argument were used to prove that a class of fractional differential equations has at least one nontrivial solution, and the existence of positive solutions for this class was established.
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Application of fractional calculus in the dynamics of beams
TL;DR: In this paper, a viscoelastic beam obeying a fractional differentiation constitutive law is considered and the governing equation is derived from the visco-elastic material model.
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Noether symmetries and conserved quantities for fractional forced Birkhoffian systems
TL;DR: In this paper, a new fractional Pfaff-Birkhoff variational principle with Riemann-Liouville derivatives and generalized force is established, from which the fractional forced Birkhoff equations are derived.
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Existence and symmetric result for Liouville–Weyl fractional nonlinear Schrödinger equation
TL;DR: The existence of positive solution for the one dimensional Schrodinger equation with mixed Liouville–Weyl fractional derivatives with radial symmetry property is studied.
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Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas
Quansheng Liu,Liguo Chen +1 more
TL;DR: The effects of the phase speed, electron number density, and the fractional order on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.
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.