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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Investigation of non-isothermal electron effects on the dust acoustic waves in four components dusty plasma
TL;DR: In this paper, the effects of the time fractional order (β), the ratio of dust to ion temperature, the mass and charge ratio (α), the non-isothermal parameter (γ) and wave velocity (v) on the DA solitary wave were studied.
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A new approach on fractional variational problems and Euler-Lagrange equations
TL;DR: It is proved the existence of minimizers for the variational problems which satisfy the Euler–Lagrange equations with Riemann–Liouville boundary conditions.
Calculus of Variations with Classical and Fractional Derivatives
TL;DR: In this paper, a proper fractional extension of the classical calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems is given. Necessary optimality conditions of the Euler-Lagrange type for variational problems containing both classical and fractions are proved.
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Numerical solution of composite left and right fractional Caputo derivative models for granular heat flow
TL;DR: In this article, a numerical scheme based on a fractional trapezoidal method for solution of fractional equation with composition of the left and right Caputo derivatives is proposed. But the numerical results are compared with analytical solutions.
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Time-fractional effect on dust-acoustic double-layer waves in four-component dusty plasma
TL;DR: In this article, the effect of the ions (electrons) kappa parameter and the ratio between temperatures of positive dust grains σ and that for ions studied, where the effects of ions kappa parameters k i on the amplitude and steepness of the double layers is more effective that both electrons and ions.
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.