Work

Degenerate Appell sequences via Caputo-type fractional difference operator

Year: 2026

Type: article

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.

Source: Rendiconti del Circolo Matematico di Palermo Series 2

DOI: 10.1007/s12215-026-01458-y

Authors: Stiven Díaz, William Ramírez, Yamilet Quintana, Clemente Cesarano

Institutions: UniNettuno University, Institute of Mathematical Sciences, Universidad Carlos III de Madrid, Universidad Autónoma de Madrid

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W7204187097