Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative

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Fractional calculus of variations for a combined Caputo derivative (2011, background): “We emphasize that this derivative allows to describe a more general class of variational problems and, as a particular case, we get the results of [2].”
Fractional hamilton formalism within caputo’s derivative (2006, methodology): “Am ong m athem aticians,RL fractionalderivativeshavebeen popularlargely because they are am enable to m any m athem aticalm anipulations.”
Fractional Variational Calculus with Classical and Combined Caputo Derivatives (2011, background): “In the particular case when the Lagrangian does not depend on the classical derivatives, γ = 1, N = 1, and we have boundary conditions (10), then one obtains from Theorem 15 the following result of [1].”
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].”
The Variable-Order Fractional Calculus of Variations (2018, background): “Agrawal continued the study of the fractional Euler–Lagrange equations (Agrawal, 2002, 2006, 2007), for some kinds of fractional variational problems, for example, problems with only one dependent variable, for functionals with different orders of fractional derivatives, for several functions,…”