Extended two-variable Fubini-type polynomials and their properties

This paper introduces a novel family of two-variable Fubini-type polynomials utilizing the two-parameter Mittag-Leffler function. The proposed approach also leads to the introduction of a new type of Stirling numbers of the second kind. The paper systematically explores various intriguing properties associated with the introduced polynomials and numbers. The analytical properties, including differential formulas, summation formulas, and connections to well-known polynomials and numbers, are thoroughly investigated and presented.