Singular integral equation involving a multivariable analog of Mittag-Leffler function

Abstract

Motivated by the recent work of the second author (Özarslan in Appl. Math. Comput. 229:350-358, 2014), we present, in this paper, some fractional calculus formulas for a mild generalization of the multivariable Mittag-Leffler function, a Schläfli's type contour integral representation, some multilinear and mixed multilateral generating functions; and, finally, we consider a singular integral equation with the function [InlineEquation not available: see fulltext.] in the kernel and we provide its solution. MSC: 26A33, 33E12.