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Explicit evaluations of matrix-variate gamma and beta integrals in thecomplex domain by using conventional procedures is extremely difficult. Such anevaluation will reveal the structure of these matrix-variate integrals. In thisarticle, explicit evaluations of matrix-variate gamma and beta integrals in thecomplex domain for the order of the matrix p = 1; 2 are given. Then fractionalintegral operators of the Kober type are given for some specific cases of thearbitrary function. A formal definition of fractional integrals in the complexmatrix-variate case was given by the author earlier as the M-convolution ofproducts and ratios, where Kober operators become a special class of fractionalintegral operators.

Evaluation of Matrix-variate Gamma and Beta Integrals as Multiple  Integrals and Kober Fractional Integral Operators in the Complex Matrix  Variate Case