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Generalized integral transform and fractional calculus involving extended \(_p R_q(\alpha, \beta; z)\) function. (English) Zbl 1499.33052

Summary: In this paper, we address an extended version of \(_p R_q(\alpha, \beta; z)\) function using \(k\)-Pochhammer symbol and study their classical properties and generalized integral transform. Further, we study Pathway fractional hypergeometric integral and fractional derivatives of the extended \(_p R_q(\alpha, \beta; z)\) function. Some special cases have also been illustrated.

MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
44A20 Integral transforms of special functions
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