RT journal article
T1 On proportional hybrid operators in the discrete setting
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 and Poisson transformation
K1 discrete Laplace
K1 fractional Caputo and Riemann–Liouville operators
K1 Laplace
K1 Mittag-Leffler functions and sequences
K1 proportional hybrid operators
K1 Toeplitz operators
AB In this article, we introduce a new nonlocal operator (Formula presented.) defined as a linear combination of the discrete fractional Caputo operator and the fractional sum operator. A new dual operator (Formula presented.) is also introduced by replacing the discrete fractional Caputo operator with the discrete fractional Riemann–Liouville operator. It is shown that it corresponds to a natural discretization of a proportional hybrid operator defined by the Riemann–Liouville operator instead of Caputo hybrid operator. We then analyze the most important properties of these operators, such as their inverse operator and the (Formula presented.) -transform, among others. As an application, we solve difference equations equipped with these operators and obtain explicit solutions for them in terms of trivariate Mittag-Leffler sequences.
PB John Wiley and Sons Ltd
SN 1099-1476
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35599
UL http://hdl.handle.net/10498/35599
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026