Erdélyi-Kober Fractional Integrals in the Complex Domain
In Chaps. 2, 3, 4, and 5 we considered the real scalar variable case, real multivariate case, real one matrix-variate case, real several matrix-variate case. In the present chapter we will look into fractional calculus in the complex domain. Since we will be dealing with p × p Hermitian positive definite matrices, for p = 1 Hermitian positive definite means a real scalar positive variable. Hence we start with p ≥ 2. Fractional calculus of one real scalar variable case is the one most frequently appearing in various theoretical and applied areas. Fractional calculus in the complex domain was considered only recently, see Mathai . The following discussion is based on this work.
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