Bull. Korean Math. Soc. 2018; 55(2): 599-610
Online first article January 12, 2018 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b170193
Copyright © The Korean Mathematical Society.
Junesang Choi, Rakesh K. Parmar
Dongguk University, Government College of Engineering and Technology
We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving $(p, q)$-extended Bessel function $J_{\nu,\,p,q} (z)$, which are expressed in terms of Hadamard product of the $(p, q)$-extended Gauss hypergeometric function and the Fox-Wright function $_{p}\Psi_{q}(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.
Keywords: $(p, q)$-extended Bessel function, $(p,q)$-extended hypergeometric function, Fox-Wright function, fractional calculus operators, Hadamard product
MSC numbers: Primary 26A33, 33B20, 33C20; Secondary 26A09, 33B15, 33C05
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