Degenerate Appell sequences via Caputo-type fractional difference operator

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 ∇ _λ ^α ∇ λ α -Appell sequences, are constructed for $$0<$$ 0 < α ≤ 1 α ≤ 1 and λ >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.