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
More filters
Journal ArticleDOI
Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods
TL;DR: In this article, the authors discuss thermodynamic restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders, and derive entropy inequality for isothermal processes.
Journal ArticleDOI
Formulation and solution of space–time fractional Boussinesq equation
S.A. El-Wakil,Essam M. Abulwafa +1 more
TL;DR: In this article, a semi-inverse method is used to find the Lagrangian of the Boussinesq equation, where the classical derivatives in the Lagrangeian are replaced by the fractional derivatives.
Journal ArticleDOI
Time-fractional KdV equation for plasma of two different temperature electrons and stationary ion
TL;DR: Using the time-fractional KdV equation, the nonlinear properties of small but finite amplitude electron-acoustic solitary waves are studied in a homogeneous system of unmagnetized collisionless plasma as mentioned in this paper.
Journal ArticleDOI
Fractional Euler–Lagrange equations revisited
TL;DR: In this paper, the necessary and sufficient optimality conditions for the Euler-Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann-Liouville sense were presented.
Journal Article
On a Differential Equation with Left and Right Fractional Derivatives
TL;DR: In this paper, the fractional order differential equation with Riemann-Liouville fractional derivatives is treated as the Euler-Lagrange equation in variational principles.
References
More filters
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.