Communications in Numerical Analysis 2017 No.2 (2017) 101-108 Available online at www.ispacs.com/cna Volume 2017, Issue 2, Year 2017 Article ID cna-00314, 8 Pages doi:10.5899/2017/cna-00314 Research Article Marichev-Saigo Integral Operators Involving the Product of K-Function and Multivariable Polynomials D. L. Suthar 1∗ , Haile Habenom 1 (1) Department of Mathematics, College of Natural Sciences, Wollo University, Dessie, Ethiopia Copyright 2017 c ⃝ D. L. Suthar and Haile Habenom. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The aim of this paper to establish the Marichev-Saigo-Maeda fractional integration formula to the product of the K-function with the general class of multivariable polynomials. The results are presented in terms of the Wright generalized hypergeometric function. Corresponding assertions in terms of Saigo, Erd ´ elyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Further, we point out also their relevance. Keywords: Generalized fractional integral operators, K-function, Wright function, general class of multivariable polynomials. 2010 Mathematics Subject Classification: 26A33, 33C05, 33C10, 33C20. 1 Introduction Fractional calculus is a branch of classical mathematics, formulated in 1695. After long time, fractional calculus was not very popular among science and engineering community and was regarded as a pure mathematical realm without real applications. Now the field of fractional calculus is undergoing rapid developments with more and more convincing applications in the real world. Various authors Baleanu et al. [2], Kilbas [5], Kiryakova ([6],[7]), Kumar et al. [8], Samko et al. [14] and Suthar et al. [22] etc. investigated on the field of fractional calculus and its applications. Several motivating results which are significant to the present work are also obtained. A generalization of the hyper- geometric fractional integrals for α , α ′ , β , β ′ , δ ∈ C and ℜ(δ ) ∈ C, is introduced by Marichev [9] as follows: ( I (α,α ′ ,β ,β ′ ,δ ) 0+ f ) (x)= x −α Γ (δ ) ∫ x 0 (x − t ) δ −1 t −α ′ F 3 ( α , α ′ , β , β ′ ; δ ;1 − (t /x), 1 − (x/t ) ) f (t )dt , (1.1) ( I (α,α ′ ,β ,β ′ ,δ ) − f ) (x)= x −α ′ Γ (δ ) ∫ ∞ x (t − x) δ −1 t −α F 3 ( α , α ′ , β , β ′ ; δ ;1 − (x/t ), 1 − (t /x) ) f (t )dt , (1.2) In (1.1) and (1.2), F 3 (.) denotes the Appell function (also known as Horn function) which is introduced by Srivastava and Karlson [21] p F q (α , α ′ , β , β ′ ; δ ; x; y)= ∞ ∑ m,n=0 (α ) m (α ′ ) n (β ) m (β ′ ) n (δ ) m+n m! n! x m y n , max {|x| , |y|} < 1, (1.3) ∗ Corresponding author. Email address: dlsuthar@gmail.com, Tel:+251943740753 101