Hamilton-Jacobi formulation for systems in terms of Riesz's fractional derivatives

DOI10.1007/s10773-011-0668-3zbMath1216.35164OpenAlexW1980410947MaRDI QIDQ539634

Eqab M. Rabei, Ibrahim M. Rawashdeh, Dumitru Baleanu, Sami I. Muslih

Publication date: 30 May 2011

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-011-0668-3

zbMATH Keywords

Lagrangian formulationHamiltonian formulationfractional calculus of variationHamilton-Jacobi formulationRiesz fractional derivatives

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fractional partial differential equations (35R11)

Related Items (10)

Generalized fractional calculus with applications to the calculus of variations ⋮ A fast numerical method for two-dimensional Riesz space fractional diffusion equations on a convex bounded region ⋮ Fast implicit integration factor method for nonlinear space Riesz fractional reaction-diffusion equations ⋮ Quantization of the damped harmonic oscillator ⋮ Numerical solution of multidimensional time‐space fractional differential equations of distributed order with Riesz derivative ⋮ Dynamical modeling and physical analysis of pipe flow in hydraulic systems based on fractional variational theory ⋮ Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model ⋮ The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations ⋮ Adiabatic invariants for generalized fractional Birkhoffian mechanics and their applications ⋮ Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix

Cites Work

• Unnamed Item
• Unnamed Item
• Recent history of fractional calculus
• The Hamilton formalism with fractional derivatives
• Quantization of Brownian motion
• New applications of fractional variational principles
• Fractional Hamiltonian analysis of irregular systems
• Fractals and fractional calculus in continuum mechanics
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
• Describing function analysis of systems with impacts and blacklash
• Formulation of Hamiltonian equations for fractional variational problems.
• An efficient method for solving systems of fractional integro-differential equations
• A general formulation and solution scheme for fractional optimal control problems
• Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative
• A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Fractional variational calculus in terms of Riesz fractional derivatives
• Lagrangian Formulation of Classical Fields within Riemann-Liouville Fractional Derivatives
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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