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