Operational perspective on degenerate Gould–Hopper–Fubini polynomials using fractional calculus

Abstract This paper serves as a bridge between the fractional and operational approaches to construct a new type of trivariate degenerate Gould–Hopper–Fubini polynomials. It presents the method of evaluating operational results, including important identities, differential operators, and operational representations, which serve as a useful tool for generating fractional-order generalized degenerate Gould–Hopper–Fubini polynomials by exploiting fractional operators. This approach provides a broad platform for exploring the study of generalized special polynomials of fractional order. Additionally, explicit series representations and summation formulas for these polynomials are derived.