Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent
From MaRDI portal
Publication:2514044
DOI10.1007/s40314-013-0053-3zbMath1348.70076OpenAlexW2078783688MaRDI QIDQ2514044
Publication date: 30 January 2015
Published in: Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40314-013-0053-3
non-standard Lagrangiansfractional action-like variational approachfractional oscillatorstime-dependent fractional exponent
Fractional derivatives and integrals (26A33) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Variational principles of physics (49S05)
Related Items (23)
Research on early warning algorithm for economic management based on Lagrangian fractional calculus ⋮ Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise ⋮ Noether symmetries and conserved quantities for fractional forced Birkhoffian systems ⋮ Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator ⋮ Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way ⋮ Noether theorem and its inverse for nonlinear dynamical systems with nonstandard Lagrangians ⋮ Fractional Tikhonov regularization method in Hilbert scales ⋮ Space-time fractional nonlinear partial differential equations: symmetry analysis and conservation laws ⋮ Unnamed Item ⋮ Fractional functional with two occurrences of integrals and asymptotic optimal change of drift in the Black-Scholes model ⋮ Analysis and applications of sequential hybrid \(\psi\)-Hilfer fractional differential equations and inclusions in Banach algebra ⋮ Non-standard Lagrangians with higher-order derivatives and the Hamiltonian formalism ⋮ From classical to discrete gravity through exponential non-standard Lagrangians in general relativity ⋮ Noether's theorems for dynamical systems of two kinds of non-standard Hamiltonians ⋮ Non-standard fractional Lagrangians ⋮ Non-standard Lagrangians in rotational dynamics and the modified Navier-Stokes equation ⋮ Conserved quantities for Hamiltonian systems on time scales ⋮ Classical string field mechanics with non-standard Lagrangians ⋮ Non-standard magnetohydrodynamics equations and their implications in sunspots ⋮ Applying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equations ⋮ Complex Lie algebroids and Finsler manifold in time-dependent fractal dimension and their associated decomplexifications ⋮ Non-standard power-law Lagrangians in classical and quantum dynamics ⋮ A generalized nonlinear oscillator from non-standard degenerate Lagrangians and its consequent Hamiltonian formalism
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fractional variational problems from extended exponentially fractional integral
- A periodic functional approach to the calculus of variations and the problem of time-dependent damped harmonic oscillators
- General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems
- Generalized variational calculus in terms of multi-parameters fractional derivatives
- Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation
- Calculus of variations with fractional derivatives and fractional integrals
- The Hamilton formalism with fractional derivatives
- Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- The second-order Klein-Gordon field equation
- Variable order and distributed order fractional operators
- Fractional integration and differentiation of variable order
- Fractional integration operator of variable order in the Hölder spaces \(H^{\lambda (x)}\)
- Fractional Euler-Lagrange equations revisited
- On the variable order dynamics of the nonlinear wake caused by a sedimenting particle
- Energy evolution in the time-dependent harmonic oscillator with arbitrary external forcing
- Nonstandard Lagrangian tori and pseudotoric structures
- Reiterated homogenization of non-standard Lagrangians
- Lagrangian and Hamiltonian dynamics with imaginary time
- Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
- The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
- Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability
- A simple and unified approach to identify integrable nonlinear oscillators and systems
- Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
- Quantal phase factors accompanying adiabatic changes
- On Mathieu equation with damping
- One-parameter squeezed Gaussian states of a time-dependent harmonic oscillator and the selection rule for vacuum states
- Mechanics with variable-order differential operators
- On Dissipative Systems and Related Variational Principles
- The Inverse Variational Problem in Classical Mechanics
- Some properties of WKB series
- Integration and differentiation to a variable fractional order
- Exact Quantization Conditions. II
- Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)
- Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients
- Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
- Nonintegrability of the two-body problem in constant curvature spaces
- Fractional actionlike variational problems
- FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS
- On the inverse problem of the calculus of variations
This page was built for publication: Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent