Degenerate Appell sequences via Caputo-type fractional difference operator
Abstract In this article, we define and study a novel class of function sequences based on their relationship with fractional-order difference operators in the Caputo sense. These sequences, known as $$\nabla _\lambda ^\alpha $$ ∇ λ α -Appell sequences, are constructed for $$0<$$ 0 < $$\alpha \le 1$$ α ≤ 1 and $$\lambda >0$$ λ > 0 . The terms of these sequences involve combinations of monomials with fractional powers and exhibit unique properties that extend classical results in the context of fractional calculus and difference operators.
Authors
- William B. Ramirez (ORCID: https://orcid.org/0000-0003-4675-0221)
- Clemente Cesarano (ORCID: https://orcid.org/0000-0002-1694-7907)
- Yamilet Quintana (ORCID: https://orcid.org/0000-0003-1053-0892)
- Stiven Díaz (ORCID: https://orcid.org/0000-0001-9613-9469)
Institutions
- Uninett (Norway) (NO)
- Martin University (US)
- Institute of Mathematical Sciences (ES)
- Universidad Carlos III de Madrid (ES)
- Universidad Autónoma de Madrid (ES)
Publication Details
- Journal
- Rendiconti del Circolo Matematico di Palermo Series 2
- Published
- 2026-08-25
- DOI
- https://doi.org/10.1007/s12215-026-01458-y
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00