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Fractional Euler-Lagrange differential equations via Caputo derivatives
Ricardo Almeida, Agnieszka B. Malinowska, Delfim F. M. Torres
We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and r…
Nondifferentiable variational principles in terms of a quantum operator
Ricardo Almeida, Delfim F. M. Torres
We develop Cresson's nondifferentiable calculus of variations on the space of Hölder functions. Several quantum variational problems are considered: with and without constraints, w…
Isoperimetric problems of the calculus of variations with fractional derivatives
Ricardo Almeida, Rui A. C. Ferreira, Delfim F. M. Torres
In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of th…
Fractional variational calculus for nondifferentiable functions
Ricardo Almeida, Delfim F. M. Torres
We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractiona…
Fractional variational problems depending on indefinite integrals
Ricardo Almeida, Shakoor Pooseh, Delfim F. M. Torres
We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main resu…