Variational formulations of differential equations and asymmetric fractional embedding
From MaRDI portal
Publication:641659
DOI10.1016/j.jmaa.2011.07.022zbMath1250.49024OpenAlexW1999508879MaRDI QIDQ641659
Publication date: 24 October 2011
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.07.022
dynamical systemsdifferential equationscalculus of variationsfractional calculusleast action principleclassical mechanics
Optimality conditions for problems involving partial differential equations (49K20) Fractional partial differential equations (35R11)
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Cites Work
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- Variational formulations of differential equations and asymmetric fractional embedding
- A formulation of Noether's theorem for fractional problems of the calculus of variations
- Formulation of Euler-Lagrange equations for fractional variational problems
- Fractional diffusion and wave equations
- Discrete mechanics and variational integrators
- Fractional embedding of differential operators and Lagrangian systems
- Stochastic embedding of dynamical systems
- A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
- The fractional diffusion equation
- Dissipative Dynamical Systems
- On Dissipative Systems and Related Variational Principles
- Lagrangian for the convection–diffusion equation
- Advances in Fractional Calculus
- Lagrangian Formulation of Classical Fields within Riemann-Liouville Fractional Derivatives
- Geometric Numerical Integration
- Homogeneous fractional embeddings
- Long way from the FPU-problem to chaos
- The random walk's guide to anomalous diffusion: A fractional dynamics approach