Fractional integral operators involving many matrix variables

Fractional integral operators of the first and second kind in many and complex matrix-variate cases are the main topic of discussion here. After discussing fractional integral operators in the real scalar variable case, the ideas are extended to fractional integral operators involving one matrix variable in the real and complex cases. Then these ideas are extended to define fractional integrals of the first and second kinds in many matrix variables in the real as well as complex cases.