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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Proceedings ArticleDOI
Mathematical Modeling and Control of Multifractal Workloads for Data-Center-on-a-Chip Optimization
TL;DR: This work proposes a complex dynamical modeling approach that captures the observed multi-fractal characteristics of inter-event times between successive workload changes and the magnitude of the increments in DCoC workloads, and investigates the impact of the multi-Fractal spectrum richness on the performance of the control algorithm.
Journal ArticleDOI
Some new existence results for fractional difference equations
TL;DR: In this paper, the authors introduced several existence theorems for a discrete fractional boundary value problem with Dirichlet boundary conditions in the case where the order ν of the fractional difference satisfies 1 < ν ≤ 2.
Journal ArticleDOI
Fractional variational calculus for nondifferentiable functions
TL;DR: It is proved necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative are proved.
Journal ArticleDOI
Conservation laws for certain time fractional nonlinear systems of partial differential equations
Komal Singla,R. K. Gupta +1 more
TL;DR: In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.
Journal ArticleDOI
Symmetries and conserved quantities for fractional action-like Pfaffian variational problems
TL;DR: In this paper, the fractional Pfaffian variational problems and fractional Noether theory are studied under a fractional model presented by El-Nabulsi, and the definitions and criteria of the Noether symmetric transformations are given, which are based on the invariance of El Nabulsis-Pfaffian action under the infinitesimal transformations of group.
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.