Leila Khitri-Kazi-Tani, Hacen Dib

A New h-Discrete Fractional Operator, Fractional Power and Finite Summation of Hypergeometric Polynomials

abstract:
In the present paper, we introduce the discrete fractional trapezoidal operators $T_{h}^{\alpha}$ for $\alpha \in (0,1)$ as the fractional power of the classical trapezoidal formula. Consequently, we derive the fractional power of a triangular matrix. As applications, we determine the eigenvectors of $T_{h}^{\alpha}$ and a finite summation formula of the product of hypergeometric polynomials.

Mathematics Subject Classification: 26A33, 39A12, 33C05, 33C45, 47B12, 15A16

Key words and phrases: Discrete fractional calculus, trapezoidal operator, hypergeometric polynomials, sectorial operator, fractional power, matrix function, Meixner polynomials