128 citations · 455 across the 16 of their papers we have counts for
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Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay
Gastao S. F. Frederico, Tatiana Odzijewicz, Delfim F. M. Torres
We obtain a nonsmooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions,…
Variable Order Fractional Variational Calculus for Double Integrals
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of G…
Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives
Loïc Bourdin, Tatiana Odzijewicz, Delfim F. M. Torres
We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann-Liouville fractional integrals, classical and Caputo fractional…
Green's Theorem for Generalized Fractional Derivatives
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is prove…
Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and der…
Generalized fractional calculus with applications to the calculus of variations
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula…