文章基本信息

标题：A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators
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作者：Ayşegül Çetinkaya ; İ. Onur Kıymaz ; Praveen Agarwal 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：156
DOI：10.1186/s13662-018-1612-0
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters. We also define new generalizations of the Gauss F, Appell F 1 $F_)$ , F 2 $F_,$ and Lauricella F D 3 $F_{D}^"$ hypergeometric functions with the help of new beta function. Then we obtain some generating function relations for these generalized hypergeometric functions by using each generalized fractional operators, separately. One of the purposes of the present investigation is to give a chance to the reader to compare the results corresponding to each generalized fractional operators.
关键词：Beta function ; Hypergeometric functions ; Fractional operators ; Generating functions