The Hamilton formalism with fractional derivatives

By E. Rabei, K. I. Nawafleh, Raed S. Hijjawi, S. Muslih, Dumitru Băleanu. 2007

203 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6563112e4a7dc60c3fe6796e873a467baa9066ce

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Citations in the corpus

On exact solutions of a class of fractional Euler–Lagrange equations (2007, background): “During the last years the fractional variational principles [12, 13, 14, 15, 16, 17, 18, 19, 20 , 21, 22, 23, 24, 25] have developed and applied to fractional optimal control problems [26, 27].”
A fractional calculus of variations for multiple integrals with application to vibrating string (2010, background): “For applications of the fractional calculus of variations we refer the reader to [16, 17, 20, 27, 32, 36, 37, 40].”
Optimality conditions and a solution scheme for fractional optimal control problems (2009, background): “38, 2004) and the following papers: Baleanu and Akvar (2004), Rabei et al. (2007 ) a nd Atanackovic et al. (2008).”
The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems (2011, background): “Also we refer the interested reader to Kilbas et al. (2006) and Samko et al. (1993) for fractional differential equations and to Agrawal and Baleanu (2007), Baleanu (2009a,b), and Rabei et al. (2007) for some recent research works on fractional optimal control problems.”
Variational problems with fractional derivatives: Euler–Lagrange equations (2008, methodology): “applied the fractional Euler-Lagrange equations to examine fractional Lagrangian and Hamiltonian systems linear in velocities. Other applications of fractional variational principles are presented in [4, 5, 6, 9, 10, 12, 23, 24, 26, 27, 29]. We cite here also the work of G. S. F. Frederico and D. F.”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, background): “Fractional derivatives play an increasing role in mathematics, physics and engineering [4, 16, 17, 21, 24, 29] and the theory of the calculus of variations has been extended in order to deal with more general systems containing noninteger derivatives [1, 2, 3, 5, 9, 11, 19, 26, 27].”
Fractional variational optimal control problems with delayed arguments (2010, background): “Fractional calculus is as old as the classical calculus, and during the last decades it has become a serious candidate in solving problems of complex systems which appear frequently in various branches of science and engineering [1–14].”
Fractional calculus of variations for a combined Caputo derivative (2011, background): “[15], and [22, 23]. Besides mathematics, fractional derivatives and integrals appear in physics, mechanics, engineering, elasticity, dynamics, control theory, economics, biology, chemistry, etc. (cf. [9, 13, 30, 36] and references therein). The FC is nowadays covered by several books (e.g., [21, 24,”
Fractional Optimal Control Problems with Several State and Control Variables (2010, unknown): “…and Klafter, 2000 Agrawal, 2001 Tenreiro-Machado, 2001 Agrawal, 2002 Agrawal et al., 2004 Agrawal, 2005 Baleanu and Muslih, 2005 Muslih and Baleanu, 2005 Baleanu et al., 2006 Magin, 2006 Agrawal, 2007a,b El-Nabulsi and Torres, 2007 Rabei et al., 2007 Vinagre and Feliu, 2007 Tricaud and Chen, 2008).”