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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Journal ArticleDOI
Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach
TL;DR: In this paper, a frequency distributed representation of fractional differential equations called the infinite state approach is proposed, associated with an original formulation of the fractional energy, which is intended to really control the internal system state.
Journal ArticleDOI
Erratum to “Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications”
TL;DR: In this article, the authors examined conservation laws with conformable derivative for certain nonlinear partial differential equations (PDEs) and introduced a new conservation theorem to the construction of nonlocal conservation laws for the governing systems of equation.
Posted Content
On the asymptotic integration of a class of sublinear fractional differential equations
TL;DR: In this article, the authors estimate the growth in time of the solutions to a class of nonlinear fractional differential equations with slowly-decaying coefficients, and show that in some circumstances such an estimate is optimal.
Dissertation
Solving Degenerate Stochastic Kawarada Partial Differential Equations via Adaptive Splitting Methods
TL;DR: In this article, Padgett et al. explored and analyzed highly effective and efficient computational procedures for solving a class of nonlinear and stochastic partial differential equations with degenerate Kawarada equations.
Proceedings ArticleDOI
On the boundary conditions in modeling of human-like reaching movements
TL;DR: This paper shows that the conventional imposition of the boundary conditions does not always produce a good match to the experimental data featuring the acceleration jumps in highly dynamic tasks, and reformulates the problem, using the concept of natural boundary conditions, and suggests how not only the acceleration but all the boundary Conditions can placed in a natural way.
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.