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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Soliton solutions for the time-fractional nonlinear differential-difference equation with conformable derivatives in the ferroelectric materials
Journal ArticleDOI
Nonlinear Functional Analysis of Boundary Value Problems: Novel Theory, Methods, and Applications
TL;DR: In this article, Hongawi et al. showed that the existence of positive solutions for nonhomogeneous A-harmonic equations with variable growth in a Banach space can be established under certain conditions.
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Dynamic Programming for Fractional Discrete-time Systems.
TL;DR: In this article, the optimal dynamic programming problem for fractional discrete-time systems with quadratic performance index has been formulated and solved, and a new method for numerical computation of optimal programming problem has been presented.
Posted Content
A Fractional Variational Approach for Modelling Dissipative Mechanical Systems: Continuous and Discrete Settings
TL;DR: The restricted fractional Euler-Lagrange equations as mentioned in this paper are invariant under linear change of variables in the continuous and discrete settings of a Lagrangian system with respect to a particular restriction upon the admissible variation of the curves.
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Fractional calculus of variations: a novel way to look at it
TL;DR: In this article, the original fractional calculus of variations problem has been studied in a somewhat different way, and it has been shown that a fractional generalization of a classical problem has a solution without any restrictions on the derivative-order α.
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.