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Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems

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  • EL-Nabulsi, Ahmad Rami

Abstract

We communicate through this work the fractional calculus of variations and its corresponding Euler–Lagrange equations in 1D constrained holonomic, non-holonomic, and semi-holonomic dissipative dynamical system. The extension of the laws obtained to the 2D space state is done. Some interesting consequences are revealed.

Suggested Citation

  • EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:52-61
    DOI: 10.1016/j.chaos.2008.10.022
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
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    6. Nottale, L., 2005. "On the transition from the classical to the quantum regime in fractal space–time theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 797-803.
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    Cited by:

    1. EL-Nabulsi, Ahmad Rami, 2009. "Fractional Nottale’s Scale Relativity and emergence of complexified gravity," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2924-2933.
    2. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Pavlos, E.G. & Iliopoulos, A.C. & Sarafopoulos, D.V., 2014. "Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 58-95.
    3. Zhang, Yi & Jia, Yun-Die, 2023. "Generalization of Mei symmetry approach to fractional Birkhoffian mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Song, Chuan-Jing & Zhang, Yi, 2017. "Conserved quantities for Hamiltonian systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 24-36.
    5. Rami, El-Nabulsi Ahmad, 2009. "Fractional illusion theory of space: Fractional gravitational field with fractional extra-dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 377-384.
    6. El-Nabulsi, Ahmad Rami, 2009. "Complexified quantum field theory and “mass without mass” from multidimensional fractional actionlike variational approach with dynamical fractional exponents," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2384-2398.

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