8 research outputs found
Generalized transversality conditions for the Hahn quantum variational calculus
We prove optimality conditions for generalized quantum variational problems
with a Lagrangian depending on the free end-points. Problems of calculus of
variations of this type cannot be solved using the classical theory
The diamond integral on time scales
We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder’s, Cauchy–Schwarz’s, and Minkowski’s inequalities
The fuzzy Henstock–Kurzweil delta integral on time scales
We investigate properties of the fuzzy Henstock–Kurzweil delta integral (shortly, FHK Δ -integral) on time scales, and obtain two necessary and sufficient conditions for FHK Δ -integrability. The concept of uniformly FHK Δ -integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK Δ -integral.publishe