731 citations · 12.8k across the 413 of their papers we have counts for
22 papers · 1 filter
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.
Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres
We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the e…
Multiobjective fractional variational calculus in terms of a combined Caputo derivative
Agnieszka B. Malinowska, Delfim F. M. Torres
The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic…
Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives
Moulay Rchid Sidi Ammi, Delfim F. M. Torres
In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and unique…
Fractional variational calculus of variable order
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while…