Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

Abstract

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.

9 pages

References in corpus (3)

• Hamiltonian Formalism for Space-time Non-commutative Theories
• Formulation of Hamiltonian equations for fractional variational problems
• Physical Degrees of Freedom of Non-local Theories

Cited by in corpus (37)

• Fractional Hamilton formalism within Caputo's derivative
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• Time-Fractional KdV Equation: Formulation and Solution using Variational Methods
• Fractional calculus of variations for a combined Caputo derivative
• Fractional Hamiltonian analysis of higher order derivatives systems
• Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory
• A formulation of the fractional Noether-type theorem for multidimensional Lagrangians
• Gauge invariance in fractional field theories
• Cosmological Models with Fractional Derivatives and Fractional Action Functional
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional variational calculus for nondifferentiable functions
• The fractional symmetric rigid rotor
• Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
• Fractional Herglotz Variational Principles with Generalized Caputo Derivatives
• Fractional-order derivatives in cosmological models of accelerated expansion
• Fractional Almost Kahler - Lagrange Geometry
• Hamilton-Jacobi Fractional Sequential Mechanics
• Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
• Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe
• Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
• Noether's theorem for fractional variational problems of variable order
• The mixed convolved action
• Fedosov Quantization of Fractional Lagrange Spaces
• A necessary condition of Pontryagin type for fuzzy fractional optimal control problems
• Time-Fractional Optimal Control of Initial Value Problems on Time Scales
• Fractional Calculus of Variations of Several Independent Variables
• Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• On the fractional damped oscillators and fractional forced oscillators
• Ground state solution for a class of differential equations with left and right fractional derivatives
• Existence and symmetric result for Liouville-Weyl fractional nonlinear Schrödinger equation
• Fractional Bosonic Strings
• Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in plasma
• Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation
• Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods
• Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma
• Higher order temporal finite element methods through mixed formulations