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...

We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...

Using the Wright’s generalized hypergeometric function, we investigate a class W (q, s;A,B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s;A,B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) o...

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

Series expansion methods for fractional integrals are important and useful for treating certain problems of pure and applied mathematics. The aim of the present investigation is to obtain certain new fractional calculus formulae, which involve Srivastava polynomials. Several special cases of our main findings which are also believed to be new have been given. For the sake of illustration, we po...