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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Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions
TL;DR: In this article, a new kind of coupled fractional differential system involving right Caputo and left Riemann-Liouville fractional derivatives, supplemented with nonlocal three-point coupled boundary conditions, is introduced and studied.
Boundary Value Problems of Nabla Fractional Difference Equations
TL;DR: In this paper, the authors developed the theory of the nabla fractional self-adjoint difference equation, ∇ ν a (p ∇y)(t) + q(t)y(ρ(t)) = f (t) where 0 < ν < 1.
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The action principle for dissipative systems
TL;DR: In this article, the action principle for dissipative systems proposed by Riewe was generalized by fixing the mathematical inconsistencies present in the original approach, where the Lagrangian functions depend on mixed integer order and fractional order derivatives.
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Effect of trapped electron on the dust ion acoustic waves in dusty plasma using time fractional modified Korteweg-de Vries equation
TL;DR: In this article, the time fractional modified Korteweg-de Vries (TFMKdV) equation is solved to study the nonlinear propagation of small but finite amplitude dust ion-acoustic (DIA) solitary waves in unmagnetized dusty plasma with trapped electrons.
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Fractional Dynamics of Relativistic Particle
TL;DR: In this article, the fractional dynamics of relativistic particle are discussed and conditions for fractional relativism to be a Hamiltonian system are considered, which is not the case in this paper.
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.