Formulation of Euler–Lagrange equations for fractional variational problems

By Om Prakash Agrawal. 2002

957 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/69efa72021ab07ec4bcb3928f0ca43eff2db986d

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Citations in the corpus

Some new existence results for fractional difference equations (2011, background): “One may consult, for example, Agrawal (2002), Babakhani and Daftardar-Gejji (2003), Bai and Lü (2005), Goodrich (2010b), Lakshmikantham and Vatsala (2008), Xu et al.”
Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, neutral): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”
Existence of a weak solution for fractional Euler-Lagrange equations (2012, background): “Furthermore, one can find a comprehensive literature regarding necessary optimality conditions and Noether’s theorem, see [1, 3, 4, 6, 13, 25].”
Fractional optimal control problems: a pseudo-state-space approach (2011, background): “Lixia and Agrawal (2002) propose an infinite dimensional state-space realization of a fractional derivative where the fractional dynamical equation is transformed into a set of differential equations with no fractional derivative terms and Laguerre integral formula is used to convert this set of…”
Fractional Optimal Control Problems with Several State and Control Variables (2010, neutral): “…in several fields of science and engineering (Carpinteri and Mainardi, 1997 Metzel 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…”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, methodology): “In this section we collect the well-known definitions of fractional derivatives in the sense of Riemann-Liouville and Caputo (see [1, 3, 21, 24, 29]).”
A General Formulation and Solution Scheme for Fractional Optimal Control Problems (2004, background): “Agrawal [31] extends variational calculus to fractional variational problems.”
Fractional actionlike variational problems (2008, methodology): “Different methods were used to obtain the fractional Euler-Lagrange equations and the corresponding Hamiltonian canonical equations [1, 3, 4, 5, 6, 14, 22, 23, 28, 29, 33].”
A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems (2007, methodology): “In Agrawal (2002), Agrawal presented fractional Euler–Lagrange equations for Fractional Variational Problems (FVPs).”
Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives (2010, background): “In [1] Agrawal considers the problem of finding extremals for functionals containing left and right Riemann–Liouville fractional derivatives of the form”