166 citations · 229 across the 15 of their papers we have counts for
6 papers · 1 filter
Generalized Hamilton's Principle with Fractional Derivatives
Teodor M. Atanackovic, Sanja Konjik, Ljubica Oparnica +1
We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),α)$ so that the function and the order of fractional derivative are…
Variational problems with fractional derivatives: Invariance conditions and Nöther's theorem
Teodor M. Atanackovic, Sanja Konjik, Stevan Pilipovic +1
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Nec…
Variational Problems with Fractional Derivatives: Euler-Lagrange Equations
Teodor M. Atanackovic, Sanja Konjik, Stevan Pilipovic
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integra…
Foundations of the calculus of variations in generalized function algebras
Sanja Konjik, Michael Kunzinger, Michael Oberguggenberger
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal proble…
Generalized Group Actions in a Global Setting
Sanja Konjik, Michael Kunzinger
We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis…
Group invariants in algebras of generalized functions
Sanja Konjik, Michael Kunzinger
We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth settin…