Some iterated fractional q-integrals and their applications-Reference-Cited by-同舟云学术

Some iterated fractional q-integrals and their applications

Published:2018-06-01 Issue:3 Volume:21 Page:672-695
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Cao Jian¹,Srivastava H. M.²³,Liu Zhi-Guo⁴

Affiliation:

1. Department of Mathematics Hangzhou Normal University Hangzhou City 310036, Zhejiang Province , People’s Republic of China

2. Department of Mathematics and Statistics , University of Victoria Victoria , British Columbia V 8W3R4 , Canada

3. Department of Medical Research , China Medical University Hospital China Medical University , Taichung 40402 , Taiwan , Republic of China

4. School of Math. Sciences and Shanghai Key Laboratory of PMMP East China Normal University , Shanghai 200241 , Hangzhou , People’s Republic of China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2018-0036/pdf

Reference45 articles.

1. R.P. Agarwal, Certain fractional q-integrals and q-derivatives. Proc. Cambridge Philos. Soc. 66 (1969), 365–370.

2. W.A. Al-Salam, Some fractional q-integrals and q-derivatives. Proc. Edinburgh Math. Soc. (Ser. 2) 15 (1966), 135–140.

3. W.A. Al-Salam, q-Analogues of Cauchy’s formulas. Proc. Amer. Math. Soc. 17 (1966), 616–621.

4. G.E. Andrews, Summations and transformations for basic Appell series. J. London Math. Soc. (Ser. 2) 4 (1972), 618–622.

5. G.E. Andrews, Applications of basic hypergeometric series. SIAM Rev. 16 (1974), 441–484.

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