BIVARIATE k-MITTAG-LEFFLER FUNCTIONS WITH 2D-k-LAGUERRE-KONHAUSER POLYNOMIALS AND CORRESPONDING k-FRACTIONAL OPERATORS

Abstract

In this paper, we first introduce new class of 2D-k-Laguerre-Konhauser polynomi-als, & delta;L(& alpha;,& beta;) k,n (x, y), which generalizes the 2D-Laguerre-Konhauser polynomials (see [18]). Then, we define a new family of bivariate k-Mittag-Leffler functions E(& gamma;) k,& alpha;,& beta;,& delta;(x,y) and establish the k-Riemann-Liouville double fractional integral and derivative of the functions E(& gamma;) k,& alpha;,& beta;,& delta;(x,y). Moreover, we introduce an integral operator k & epsilon;(& gamma;) & alpha;,& beta;,& delta;;& omega;1,& omega;2;a+,c+ which contains the bivariate k-Mittag-Leffler functions E(& gamma;) k,& alpha;,& beta;,& delta;(x,y) in the kernel and investigate the semigroup property of this operator. Finally, the left inverse operator of the integral operator k & epsilon;(& gamma;) & alpha;,& beta;,& delta;;& omega;1,& omega;2;a+,c+ is con-structed.