The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper, the generalized fractional integral operators involving Appell’s function F 3 ? in kernel due to Marichev–Saigo–Maeda are applied id="M3"> p , q -extended Struve function. The r...

Abstract The paper aims to generalize Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen’s identity. The general contiguous variation of Clausen’s identity is found. The related Chaundy’s identit...

We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially sm...

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms a 7→ ∑ fk(a)kx , a 7→ ∑ fkΓ(a + k)x k and a 7→ ∑ fkx k/(a)k. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Turán inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexi...

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...