A Comprehensive Study of Δ _h ‐Truncated Exponential Appell Polynomials: Properties, Fractional Operators, and Computational Aspects

ABSTRACT In this article, we introduce a new class of truncated exponential‐based Appell polynomials and investigate their key properties and identities. The study further explores their connection with the monomiality principle, providing a deeper algebraic structure. Extensions of this framework lead to the construction of truncated exponential‐based Bernoulli, Euler, and Genocchi polynomials, along with their respective properties. Further, the generating relation and operational identity for these polynomials are established using fractional operators. Numerical evaluations of these special cases are presented, and the distribution of their zeros is visualized using Mathematica. The paper concludes with a summary of results and suggestions for future research directions.