TY  - JOUR
AU  - Alqahtani, Mesfer H.
AU  - Muhyi, Abdulghani
AU  - Touati, Amel
AU  - Suhail, Muntasir
AU  - Abdalgadir, L. M.
AU  - Aldwoah, Khaled
AU  - Alsulami, Amer
PY  - 2026
TI  - Some properties of Apostol–Hermite–Kampé de Fériet–Bell–Bernoulli-type polynomials and their fractional extension
JO  - AIMS Mathematics
SP  - 12449
EP  - 12477
VL  - 11
IS  - 5
AB  - This study presents a new, generalized family of special polynomials. These polynomials are designated as the Apostol–Hermite–Kampé de Fériet–Bell–Bernoulli-type polynomials. Based on their generating function, the corresponding series expansions and summation formulas are obtained. Furthermore, determinant representation and several differential and integral representations of these polynomials are derived. The fractional extension of this polynomial family is explored, resulting in the formulation of several associated identities. Finally, the study utilizes Mathematica to deliver zero distributions and graphical representations.
UR  - https://doi.org/10.3934/math.2026512
DO  - 10.3934/math.2026512