Vol. 10(2). July 2019, No. 10, pp. 136-146.

A NOTE ON FRACTIONAL q-INTEGRALS AND APPLICATIONS TO GENERATING FUNCTIONS AND q-MITTAG–LEFFLER FUNCTION
Vol. 10 (2). July 2019, No. 10, pp. 136-146
JIAN CAO

Abstract

Motivated by the fact that fractional q-integrals play important roles in numerous sciences, it’s natural to generalize the fractional q-integrals. The main object of this paper is to build the relations between fractional q-integrals and certain generating functions for q-polynomials and to generalize two fractional q-identities of [Fract. Calc. Appl. Anal. 10(2007), 359–373.] by the method of q-difference equation. As applications, we deduce the mixed and U(n + 1) type generating functions for Predrag–Sladjana–Miomir polynomial, gain the transformational fractional q-identities and bulid the relations of fractional q-integrals and q-Mittag–Leffler function.


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