On a double integral equation including a set of two variables polynomials suggested by Laguerre polynomials

Abstract

In this paper, we introduce general classes of bivariate and Mittag-Leffler functions (Formula presented.) and Laguerre polynomials (Formula presented.). We investigate double fractional integrals and derivative properties of the above mentioned classes. We further obtain linear generating function for (Formula presented.) in terms of (Formula presented.). Finally, we calculate double Laplace transforms of the above mentioned classes and then we consider a general singular integral equation with (Formula presented.) in the kernel and obtain the solution in terms of (Formula presented.). © 2017 by Eudoxus Press, LLC, All rights reserved.