Some Iterated Fractional q-Integrals and Their Applications

Abstract

Motivated by the fact that fractional q-integrals play important roles in numerous areas of mathematical, physical and engineering sciences, it is natural to consider the corresponding iterated fractional q-integrals. The main object of this paper is to define these iterated fractional q-integrals, to build the relations between iterated fractional q-integrals and certain families of generating functions for q-polynomials and to generalize two fractional q-identities which are given in a recent work [Fract. Calc. Appl. Anal. 10 (2007), 359–373]. As applications of the main results presented here, we deduce several bilinear generating functions, Srivastava-Agarwal type generating functions, multilinear generating functions and U(n + 1) type generating functions for the Rajković-Marinković-Stanković polynomials.

On Fractional q-Extensions of Some q-Orthogonal Polynomials

“…The q-hypergeometric series, a fractional q-derivative and fractional q-integral are defined. The reader will consult the References [4,6,11,14] for more informations about these concepts and some applications.…”

“…Thus, using the definitions of the fractional Little q-Laguerre functions and the fractional q-derivative (21), combined with the transformations (4) and (6) we have:…”

“…Q-fractional calculus is the field of mathematical analysis which deals with the investigation and applications of derivatives and integrals of arbitrary (real or complex) order (see [1][2][3][4][5][6][7][8] and the references therein). It is an interesting topic having interconnections with various problems in function theory, integral and differential equations, and other branches of analysis.…”

A family of theta-function identities based upon Rα,Rβ and Rm-functions related to Jacobi’s triple-product identity

“…The list of citations, which we have included in this article, is believed to be potentially useful for indicating some of the directions for further researches and related developments on the subject-matter which we have dealt with here. In particular, the recent works by Adiga et al (see [1]- [3]), Cao et al [9], Chaudhary et al (see [10] to [16]), Hahn et al [17], and Srivastava et al (see [26], [31]- [33]) are worth mentioning here.…”

A note on generalized q-difference equations for general Al-Salam–Carlitz polynomials

“…(14.24.1) and (14.25.1)]. For further information about q-polynomials, see [18][19][20][21][22][23].…”