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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Analytical solutions for heat transfer on fractal and pre-fractal domains
Keith Davey,Robert Prosser +1 more
TL;DR: In this article, a method for the determination of analytical heat transfer solutions on pre-fractal and fractal domains is described, which is based on the construction of maps from fractal domain to the continuum, which facilitate the application of traditional solution methods.
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Fractional-Order Variational Calculus with Generalized Boundary Conditions
TL;DR: In this paper, the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points are presented.
Posted Content
Fractional Calculus of Variations for Double Integrals
TL;DR: A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions as mentioned in this paper.
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Expansion formula for fractional derivatives in variational problems
TL;DR: In this paper, Atanackovic and Stankovic proposed an expansion formula for fractional derivatives and derived a consequence of the fractional integral inequality ∫ 0 T y ⋅ 0 D t α y d t ≥ 0.
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Time-fractional study of electron acoustic solitary waves in plasma of cold electron and two isothermal ions
TL;DR: In this article, a homogeneous system of unmagnetized collisionless plasma consisting of a cold electron fluid, low-temperature ion obeying Boltzmann-type distribution and high-totemperature ion with non-thermal distribution is considered.
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.