Details Details PDF BIBTEX RIS Title Existence - uniqueness result for a certain equation of motion in fractional mechanics Journal title Bulletin of the Polish Academy of Sciences Technical Sciences Yearbook 2010 Volume 58 Issue No 4 Authors Klimek, M. Divisions of PAS Nauki Techniczne Coverage 573-581 Date 2010 Identifier DOI: 10.2478/v10175-010-0058-7 ; ISSN 2300-1917 Source Bulletin of the Polish Academy of Sciences: Technical Sciences; 2010; 58; No 4; 573-581 References Hilfer R. (2000), Applications of Fractional Calculus in Physics, doi.org/10.1142/9789812817747 ; West B. (2003), Physics of Fractional Operators. ; Agrawal O. (2004), Fractional Derivatives and Their Application: Nonlinear Dynamics. ; Metzler R. (2004), The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J. Phys, A 37. ; Magin R. (2006), Fractional Calculus in Bioengineering. ; Herrmann R. (2007), The fractional symmetric rigid rotor, J. Phys. G: Nuc. Phys, 34, 607, doi.org/10.1088/0954-3899/34/4/001 ; Sabatier J. (2007), Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering. ; Miller K. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations. ; Podlubny I. (1999), Fractional Differential Equations. ; Kilbas A. (2006), Theory and Applications of Fractional Differential Equations. ; Klimek M. (2009), On Solutions of Linear Fractional Differential Equations of a Variational Type. ; Samko S. (1993), Fractional Integrals and Derivatives. ; Riewe F. (1996), Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev, E 53, 1890. ; Riewe F. (1997), Mechanics with fractional derivatives, Phys. Rev, E 55, 3581. ; Klimek M. (2001), Fractional sequential mechanics - models with symmetric fractional derivative, Czech. J. Phys, 51, 1348, doi.org/10.1023/A:1013378221617 ; Klimek M. (2002), Lagrangean and Hamiltonian fractional sequential mechanics, Czech J. Phys, 52, 1247, doi.org/10.1023/A:1021389004982 ; Agrawal O. (2002), Formulation of Euler-Lagrange equations for fractional variational problem, J. Math. Anal. Appl, 272, 368, doi.org/10.1016/S0022-247X(02)00180-4 ; Baleanu D. (2004), Lagrangians with linear velocities within Riemann-Liouville fractional derivatives, Nuovo Cimento, 119, 73. ; Baleanu D. (2005), Formulation of Hamiltonian equations for fractional variational problems, Czech. J. Phys, 55, 633, doi.org/10.1007/s10582-005-0067-1 ; Baleanu D. (2006), Fractional Hamiltonian analysis of irregular systems, Signal Processing, 86, 2632, doi.org/10.1016/j.sigpro.2006.02.008 ; Cresson J. (2007), Fractional embedding of differential operators and Lagrangian systems, J. Math. Phys, 48, 033504, doi.org/10.1063/1.2483292 ; Agrawal O. (2006), Fractional variational calculus and the transversality conditions, J. Phys, A 39, 10375. ; Atanackovic T. (2008), Variational problems with fractional derivatives: Euler-Lagrange equations, J. Phys. A: Math. & Theor, 41, 095201. ; Tarasov V. (2006), Fractional variations for dynamical systems: Hamilton and Lagrange approaches, J. Phys. A: Math. & Gen, 39, 8409, doi.org/10.1088/0305-4470/39/26/009 ; Tarasov V. (2006), Psi-series solution of fractional Ginzburg- Landau equation, J. Phys. A: Math. & Gen, 39, 8395, doi.org/10.1088/0305-4470/39/26/008 ; Jumarie G. (2007), Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferentiable functions, Chaos, Solitons & Fractals, 32, 969, doi.org/10.1016/j.chaos.2006.07.053 ; Klimek M. (2005), Lagrangian fractional mechanics - a noncommutative approach, Czech. J. Phys, 55, 1447, doi.org/10.1007/s10582-006-0024-7 ; Agrawal O. (2007), Analytical schemes for a new class of fractional differential equations, J. Phys, A 40, 5469. ; Baleanu D. (2008), On exact solutions of a class of fractional Euler-Lagrange equations, Nonlinear Dyn, 52, 9281. ; Klimek M. (2007), Solutions of Euler-Lagrange equations in fractional mechanics, null, 1, 73. ; Klimek M. (2008), G-Meijer functions series as solutions for certain fractional variational problem on a finite time interval, J. Eu. des Systèmes Automatisés, 42, 653, doi.org/10.3166/jesa.42.653-664 ; Atanackovic T. (2007), On a class of differential equations with left and right fractional derivatives, Zamm, 87, 537, doi.org/10.1002/zamm.200710335 ; Maraaba T. (2008), Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives, J. Math. Phys, 49, 083507, doi.org/10.1063/1.2970709 ; Klimek M. (2010), On analogues of exponential functions for antisymmetric fractional derivatives, Comp. & Math. Appl, 59, 1709, doi.org/10.1016/j.camwa.2009.08.013