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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Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p -Laplacian
TL;DR: In this article, the existence of positive solutions for the nonlinear fractional boundary value problem with a p-Laplacian operator was studied and a positive solution was proposed.
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Existence of a weak solution for fractional Euler–Lagrange equations
TL;DR: In this paper, sufficient conditions for the existence of a weak solution for fractional Euler-Lagrange equations were derived, where Dα− and Dα+ are the fractional derivatives of Riemann-Liouville of order 0<α<1.
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Hamilton’s principle with variable order fractional derivatives
TL;DR: In this paper, a generalization of Hamilton's principle is proposed, in which the minimization is performed with respect to the admissible functions and the order of the derivation, and the Euler-Lagrange equations for such minimization are derived.
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Fractional variational principles with delay within caputo derivatives
TL;DR: In this article, the fractional variational principles within Caputo derivatives in the presence of delay derivatives were investigated and corresponding Euler-Lagrange equations were obtained for the case of one dependent variable.
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Fractional Optimal Control Problems With Specified Final Time
Raj Kumar Biswas,Siddhartha Sen +1 more
TL;DR: In this article, a constrained dynamic optimization problem of a fractional order system with fixed final time has been considered, and a general formulation and solution scheme of a class of fractional optimal control problems is presented.
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.