Abstract
In this article, thek-fractional-order integral and derivative operators including thek-hypergeometric function in the kernel are used for thek-Wright function; the results are presented for thek-Wright function. Also, some of special cases related to fractional calculus operators andk-Wright function are considered.
Highlights
Introduction and PreliminariesFractional calculus was introduced in 1695, but in the last two decades researchers have been able to use it properly on the account of availability of computational resources
In a series of research publications on generalized classical fractional calculus operators, research by Mubeen and Habibullah [11] has been published on the integral part of the Riemann-Liouville version and its applications; an alternative definition for the k-Riemann–Liouville fractional derivative was introduced by Dorrego [12]. e left- and right-hand operators of Saigo k-fractional integration and differentiation associated with the k-Gauss hypergeometric function defined by Gupta and Parihar [13] are as follows:
If condition (11) is satisfied and I0τ,+δ,kc be the left-sided integral operator of the generalized k-fractional integration associated with k-Wright function, the following equation holds true:
Summary
Introduction and PreliminariesFractional calculus was introduced in 1695, but in the last two decades researchers have been able to use it properly on the account of availability of computational resources. E left- and right-hand operators of Saigo k-fractional integration and differentiation associated with the k-Gauss hypergeometric function defined by Gupta and Parihar [13] (see [14]) are as follows: If condition (11) is satisfied and I0τ,+δ,,kc be the left-sided integral operator of the generalized k-fractional integration associated with k-Wright function, the following equation holds true: Ai, bj, εi1,p; ςj1,q; ctv/k⎤⎥⎥⎦⎫⎪⎬⎪⎭⎞⎟⎠(x) x(ζ− δ/k)− 1p+2Ψkq+2⎡⎢⎢⎣
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