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 Formulation of the de Broglie-Proca For Space with Noninteger Dimension
TL;DR: In this article , the Lagrangian formulation of the de Broglie-Proca (dBP) field for space with noninteger dimension is examined and the solutions of these equations are found where the dimensionality of the space is.
Existence and uniqueness of solutions for nonlinear fractional differential equations with nonlocal boundary conditions
TL;DR: In this paper, the nonlocal and integral boundary value problems for the system of nonlinear fractional difierential equations involving the Caputo fractional derivative are investigated.
Journal ArticleDOI
Formation and Shock Solutions of the Time Fractional (2+1) and (3+1)-Dimensional Boiti–Leon–Manna–Pempinelli Equations
Swapan Biswas,Uttam Ghosh +1 more
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Preview tracking control for a class of fractional-order linear systems
Fucheng Liao,Hao Xie +1 more
TL;DR: In this article, the authors studied the preview tracking control of a class of fractional-order linear systems and proposed an optimal preview controller for the augmented error system when the reference signal is previewable.
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Generalized Fuzzy Euler-Lagrange equations and transversality conditions
TL;DR: In this article, the study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced, and necessary and sufficient optimality conditions for problems of variations with free endpoints are proved, as well as transversality conditions.
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.