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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Mixed convolved action.
Gary F. Dargush,Jinkyu Kim +1 more
TL;DR: A stationary principle is developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of displacement and force variables, using temporal convolutions and fractional derivatives.
Journal Article
Fractional calculus of variations for double integrals
TL;DR: A necessary optimality condition of Euler{Lagrange type, in the form of a multitime fractional PDE, as well as a su-cient condition and fractional natural boundary conditions were proved in this paper.
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Fedosov Quantization of Fractional Lagrange Spaces
Dumitru Baleanu,Sergiu I. Vacaru +1 more
TL;DR: In this paper, a non-olonomic deformation (Fedosov type) quantization of fractional Lagrange geometries with Caputo fractional derivative is presented.
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Modeling and analysis of fractional neutral disturbance waves in arterial vessels
TL;DR: In this article, a mathematical model of neutral perturbation flow in arterial vessels has been proposed to predict and diagnose related heart disease, such as arteriosclerosis and hypertension, etc. The model established in the model can show the propagation of the disturbance flow in the radius direction.
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Solution of the Equations of Motion for Einstein's Field in Fractional D Dimensional Space-Time
Madhat Sadallah,Sami I. Muslih +1 more
TL;DR: Sadallah et al. as mentioned in this paper extended their work to obtain the equations of motion for Einstein's field in fractional dimensions of N+1 space-time coordinates, and they showed that the time dependent solutions are single valued for only 4-dimensional space.
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.