Lagrangian Formulation of Classical Fields within Riemann-Liouville Fractional Derivatives

By Dumitru Băleanu, S. Muslih. 2005

168 citations recorded by the source corpus.

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation. The fractional Euler-Lagrange equations were obtained and two examples were studied.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b16512607b1f724085c522b25d07797ad78ec211

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In Mathematical Physics

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In Numerical Analysis

Citations in the corpus

Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, unknown): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[245] D.”
On exact solutions of a class of fractional Euler–Lagrange equations (2007, unknown): “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 Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems (2007, unknown): “…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).”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, unknown): “The new fractional variational calculus provide a more realistic approach to physics [6, 7, 8, 18, 22, 28], permitting to consider nonconservative systems in a natural way—a very important issue since closed systems do not exist: forces that do not store energy, socalled nonconservative or dissipati”
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 new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives (2010, background): “During the last years, the fractional variational principles have been applied successfully in control theory [17–19] aswell as in physics [20–29].”
Fractional calculus of variations for a combined Caputo derivative (2011, unknown): “, [1, 5, 8, 12, 17, 19]), the Caputo fractional derivative (see, e.”