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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Lagrangian for the Convection-Diffusion Equation
TL;DR: Using the asymmetric fractional calculus of variations, the authors derived a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.
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Existence of solutions for Kirchhoff-type fractional Dirichlet problem with $p$-Laplacian
TL;DR: In this paper, the authors investigated the existence of solutions for a class of Laplacian fractional order Kirchhoff-type systems with Riemann-Liouville fractional derivatives and a parameter.
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Conservation laws and series solutions of variable coefficient time fractional Kawahara equation
TL;DR: In this paper, explicit power series solutions and conservation laws of variable coefficient time fractional Kawahara equation with Riemann-Liouville derivative were investigated, which describs oscillatory...
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A Central Difference Numerical Scheme for Fractional Optimal Control Problems
TL;DR: In this article, a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a fractional derivative (FD) is defined in the Riemann-Liouville sense is presented.
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Optical solitons in birefringent fibers with the generalized coupled space–time fractional non-linear Schrödinger equations
TL;DR: In this article , an integer-order generalized coupled NLS equation was introduced to describe optical solitons in birefringence fibers, and a semi-inverse and fractional variational method was used to extend the integer order model to the space-time fractional order.
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.