101 citations · 650 across the 25 of their papers we have counts for
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A symmetric quantum calculus
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
We introduce the -symmetric difference derivative and the -symmetric Nörlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generaliz…
Higher-order infinite horizon variational problems in discrete quantum calculus
Natalia Martins, Delfim F. M. Torres
We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.
Generalizing the variational theory on time scales to include the delta indefinite integral
Natalia Martins, Delfim F. M. Torres
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the in…
Higher-order Hahn's quantum variational calculus
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order.