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Variational principles and symmetries on fibered multisymplectic manifolds

References [1] V. Aldaya, J. A. de Azcarraga: Variational Principles on r - th order jets of fibre bundles in Field Theory. J. Math. Phys. 19 (9) (1978) 1869-1875. [2] V. Aldaya, J.A. de Azcarraga: Higher order Hamiltonian formalism in Field Theory. J. Phys. A 13 (8) (1980) 2545-2551. [3] V. I. Arnold: Mathematical methods of classical mechanics. Springer-Verlag, New York (1989). [4] P. Dedecker: On the generalization of symplectic geometry to multiple integrals in the calculus of variations. In

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A new class of almost complex structures on tangent bundle of a Riemannian manifold

] R. M. Friswell, C. M. Wood: Harmonic vector fields on pseudo-Riemannian manifolds. Journal of Geometry and Physics 112 (2017) 45–58. [6] S.T. Lisi: Applications of Symplectic Geometry to Hamiltonian Mechanics. PhD thesis, New York University (2006) [7] P. Petersen: Riemannian Geometry . Springer (2006). [8] E. Peyghan, A. Heydari, L. Nourmohammadi Far: On the geometry of tangent bundles with a class of metrics. Annales Polonici Mathematici 103 (2012) 229–246. [9] E. Peyghan, H. Nasrabadi, A. Tayebi: The homogenous lift to the (1, 1

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The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories

References [1] I. M. Anderson: The Variational Bicomplex. (1989). Book preprint, technical report of the Utah State University [2] M. de León,P. R. Rodrigues: Generalized Classical Mechanics and Field Theory. North-Holland, Amsterdam (1985). [3] G. Giachetta, L. Mangiarotti, G. Sardanashvily: New Lagrangian and Hamiltonian Methods in Field Theory. World Scientific, Singapore (1997). [4] I. S. Krasilschik, V. V. Lychagin, A. M. Vinogradov: Geometry of Jet Spaces and Differential Equations. Gordon

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Geometry of the free-sliding Bernoulli beam

'shchik and Vinogradov, translated from 1997 Russian original by Verbovetsky and Krasil'shchik [3] P. Dedecker: Calcul des variations, formes différentielles et champs géodésiques. In: Géométrie différentielle. Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg. Centre National de la Recherche Scientifique, Paris (1953) 17-34. [4] I. M. Gel'fand and L. A. Dikiĭ: The calculus of jets and nonlinear Hamiltonian systems. Funkcional. Anal. i Priložen. 12 (2) (1978) 8-23. ISSN 0374-1990 [5] M

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Multiplicity result for a stationary fractional reaction-diffusion equations

. [15] Mawhin J. and Willen M., Critical point theory and Hamiltonian systems, Applied Mathematical Sciences 74, Springer, Berlin, 1989. [16] Mendez A. and Torres C., Multiplicity of solutions for fractional Hamiltonian systems with Liouville-Weyl fractional derivarives, Fract. Calc. Appl. Anal., 18, No 4, 875-890, 2015. [17] Nyamoradi N., Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions, Medit. J. Math., 11(1), 75-87(2014). [18] Podlubny I., Fractional

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Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator

-dimensional superintegrability, J. Math. Phys. 46 (2005), 062703-062721. [8] V. K. Chandrasekar, S. N. Pandey, M. Senthilvelan and M. Lakshmanan, Simple and unified approach to identify integrable nonlinear oscillators and systems, J. Math. Phys. 47 (2006), 023508-023545. [9] V. K. Chandrasekar, M. Senthilvelan and M. Lakshmanan, On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator, Phys. Rev. E72 (2005), 066203-066211. [10] V. K. Chandrasekar, M. Senthilvelan and M. Lakshmanan, A Nonlinear oscillator with unusual dynamical properties, in Proceedings of

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Generalized Fuzzy Euler-Lagrange equations and transversality conditions

Briefs in Applied Sciences and Technology, Springer; 2015. [25] I. Podlubny, Fractional Differential Equations, Academic Press, New York; 1999. [26] F. Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E 53 (1996) 1890-1899. [27] S. Salahshour, T. Allahviranloo, S. Abbasbandy and D. Baleanu, Existence and uniqueness results for fractional differential equations with uncertainty, Advances in Difference Equations 2012, 112 (2012). [28] B. van Brunt, The Calculus of Variations, Springer

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