Hamiltonian formulation of systems with linear velocities within Riemann–Liouville fractional derivatives

By S. Muslih, Dumitru Băleanu. 2005

181 citations recorded by the source corpus.

Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1f1107abeab168091ad5b1d74932d91baa804cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Modeling and Simulation

In Statistical and Nonlinear Physics

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].”
Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β) (2007, methodology): “s two parameters and is wider than the standard class of Hamiltonian dynamical systems. Our approach is diﬀerent from the ones found in the literature: diﬀerent from S. Muslih and D. Baleanu approach [14], where no fractional integral action is used and no decaying friction term considered; diﬀerent”
On fractional thermoelasticity (2011, background): “chemistry, biology, modelling and identification, electronics, wave propagation, classical mechanics [22], viscoelasticity [23–27] and thermoelasticity [28–30].”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, methodology): “The fractional Euler–Lagrange equation has recently been presented in the literature (Almeida and Torres, 2009; Atanacković et al., 2007; Bastos et al., 2011; Frederico and Torres, 2007; Malinowska and Torres, 2010; Muslih and Baleanu, 2005; Stanislavsky, 2006; Tarasov and Zaslavsky, 2005, 2006).”
Variational problems with fractional derivatives: Euler–Lagrange equations (2008, background): “rresponding Euler-Lagrange equations and discussed possibilities for prescribing boundary conditions in each case. The work of mentioned authors inﬂuenced many recent papers. For instance, D. Baleanu [7, 8] applied the fractional Euler-Lagrange equations to examine fractional Lagrangian and Hamilton”
Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets (2014, background): “During recent years fractional variational principles have been developed (Baleanu and Avkar, 2004; Baleanu, 2006; Baleanu and Muslih, 2005a,b; Muslih and Baleanu, 2005).”
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].”
A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems (2007, background): “…and Avkar, 2004), fractional metafluid dynamics (Baleanu, 2004), fractional Lagrangian and Hamiltonian formulations of discrete and continuous systems (Muslih and Baleanu, 2005a 2005b Muslih et al., 2006 Baleanu and Muslih, 2005) and Hamiltonian analysis of irregular systems (Baleanu, 2006).”
Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative (2007, background): “…Lagrangians with linear velocities (Baleanu and Avkar, 2004), fractional metafluid dynamics (Baleanu, 2004), fractional Hamiltonian formulation of systems with linear velocity (Muslih and Baleanu, 2005a), and Hamiltonian equations for fractional variational problems (Muslih and Baleanu, 2005b).”