Generalized hypergeometric k-functions via (k,s)-fractional calculus

Volume 10, Issue 4, pp 1791--1800 http://dx.doi.org/10.22436/jnsa.010.04.40

Publication Date: April 20, 2017 Submission Date: February 26, 2017

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Authors

Kottakkaran Sooppy Nisar - Department of Mathematics, College of Arts and Science at Wadi Al-dawaser, Prince Sattam bin Abdulaziz University, Alkharj, Riyadh region 11991, Kingdom of Saudi Arabia. Gauhar Rahman - Department of Mathematics, International Islamic University, Islamabad, Pakistan. Junesang Choi - Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea. Shahid Mubeen - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. Muhammad Arshad - Department of Mathematics, International Islamic University, Islamabad, Pakistan.

Abstract

We introduce (\(k; s\))-fractional integral operator involving (\(k, \tau\))-hypergeometric function and the Riemann-Liouville leftsided and right-sided (\(k; s\))-fractional integral and differential operators. Then we present several useful and interesting results involving the introduced operators. Also, the results presented here, being general, are pointed out to reduce to some known results.

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Keywords

• Generalized hypergeometric function \(_pF_q\)
• \(\tau\)-hypergeometric function
• k-hypergeometric function
• differential operators
• (\(k، \tau\))-hypergeometric function
• \(k\)-Pochhammer symbol
• \(k\)-gamma function
• \(k\)-beta function
• (\(k،s\))-fractional integral.

MSC

•  33C20
•  33E20
•  26A33
•  26A99

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