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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Stability for manifolds of the equilibrium state of fractional Birkhoffian systems
TL;DR: In this paper, a new stability theory of fractional dynamics is presented, i.e., the stability for manifolds of equilibrium state of a fractional Birkhoffian system, in terms of Riesz derivatives, and explore its applications.
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On the fractional Jaulent-Miodek equation associated with energy-dependent Schrödinger potential: Lie symmetry reductions, explicit exact solutions and conservation laws
TL;DR: In this paper, the Lie symmetry analysis is performed on a coupled system of nonlinear time-fractional Jaulent-Miodek equations associated with energy-dependent Schrodinger potential.
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Fractional oscillator equation: analytical solution and algorithm for its approximate computation
TL;DR: In this article, the fractional oscillator equation in a finite time interval is considered and a numerical algorithm to approximate the solution of the considered equation is proposed, and examples of numerical solutions of this equation are given.
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Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives
Ying Zhou,Yi Zhang +1 more
TL;DR: In this paper, the generalized Pfaff-Birkhoff principle and Birkhoff's equations with classical and combined Caputo derivatives are given, and two kinds of Noether symmetry and their conserved quantities by the method of time re-parameterization.
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On Approximate Solutions for Fractional Logistic Differential Equation
Mohamed M. Khader,M.M. Babatin +1 more
TL;DR: In this paper, a new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE), which is used to reduce FLDE to solve a system of algebraic equations which is solved using a suitable numerical method.
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.