SOME ITERATED FRACTIONAL q-INTEGRALS AND THEIR APPLICATIONS
SOME ITERATED FRACTIONAL q-INTEGRALS AND THEIR APPLICATIONS
复制标题
一些迭代分数 q 积分及其应用
DOI：
10.1515/fca-2018-0036
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发表时间：
2018-06-01
影响因子：
3
通讯作者：
Liu, Zhi-Guo
中科院分区：
文献类型：
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作者：
Cao, Jian;Srivastava, H. M.;Liu, Zhi-Guo
分数阶q-积分在数学、物理和工程科学的许多领域中起着重要的作用，因此很自然地要考虑相应的迭代分数阶q-积分。本文的主要目的是定义这些迭代分数次q积分，建立迭代分数次q积分与q多项式的某些生成函数族之间的关系，并推广最近的工作[Fract.计算值应用分析10（2007），359-373]。作为本文主要结果的应用，我们导出了Rajković-Marinković-Stanković多项式的几个双线性生成函数、Srivastava-Agarwal型生成函数、多线性生成函数和U（n + 1）型生成函数.
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.