ON A DOUBLE INTEGRAL EQUATION INCLUDING A SET OF TWO VARIABLES POLYNOMIALS SUGGESTED BY LAGUERRE POLYNOMIALS - Ozarslan, M. Ali; Kurt, Cemaliye (Eudoxus Press, Llc, 2017)
In this paper, we introduce general classes of bivariate and Mittag-Leffler functions E-gamma 1,gamma 2((alpha,beta,eta,xi,lambda))(x,y) and Laguerre polynomials L-n,m((alpha,beta,gamma,eta,xi)) (x, y). We investigate double fractional integrals and derivative properties of the above mentioned classes. We further obtain linear generating function for L-n,m((alpha,beta,gamma,eta,xi))(x,y) in terms of E-gamma 1,gamma 2((alpha,beta,eta,xi,lambda))(x,y). Finally, we calculate double Laplace transforms of the above mentioned classes and then we consider a general singular integral equation with L-n,m((alpha,beta,gamma,eta,xi))(x, y) in the kernel and obtain the solution in terms of E-gamma 1,gamma 2((alpha,beta,eta,xi,lambda))(x, y).
Keywords: Double fractional integrals and derivatives; Bivariate Mittag-Leffler function; Bivariate Laguerre polynomials; Double generating functions; Singular double integral equation; Double Laplace integral