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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Stability and Controllability Study for Mixed Integral Fractional Delay Dynamic Systems Endowed with Impulsive Effects on Time Scales
TL;DR: In this article , a class of mixed integral fractional delay dynamic systems with impulsive effects on time scales is investigated, and sufficient conditions for Ulam-Hyers stability and controllability of the considered systems are established.
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Well‐posedness, optimal control and discretization for time‐fractional parabolic equations with time‐dependent coefficients on metric graphs
TL;DR: In this paper , the authors studied distributed optimal control problems governed by time-fractional parabolic equations with time dependent coefficients on metric graphs, where the fractional derivative is considered in the Caputo sense.
Posted Content
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
Jianping Zhang,Ke Chen +1 more
TL;DR: In this article, a fractional-order derivative based total α$-order variation model was proposed for image restoration, which can outperform the currently popular high order regularization models.
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Generalized Hamilton's Principle with Fractional Derivatives
TL;DR: In this article, the authors generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t)),\alpha) so that the function $y$ and the order of fractional derivative $\alpha$ are varied in the minimization procedure.
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.