Singular integral equation involving a multivariable analog of Mittag-Leffler function - Gaboury, Sebastien; Özarslan, Mehmet Ali (Springer International Publishing, 2014)
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.
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Keywords: Functional Analysis, fractional integrals and derivatives, Mathematics; Difference and Functional Equations, Partial Differential Equations; contour integral representation, singular integral equation; Mittag-Leffler function, Analysis, Ordinary Differential Equations,; Mathematics, general, APPLIED, LAGUERRE-POLYNOMIALS