31 citations · 49 across the 2 of their papers we have counts for
2 papers
math.CA2012★ 31 cited
Symmetric Differentiation on Time Scales
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on tim…
math.OC2012★ 18 cited
Hahn's Symmetric Quantum Variational Calculus
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange t…