A couple of fractional powers of Hankel-type integral transformations and pseudo-differential operators

A couple of fractional powers of Hankel-type integral transformations are discussed on certain Zemainan type spaces. The operational formulae are developed. Two variants of fractional pseudo-differential operators (FrPDO) associated with the symbol a(x, y) are defined. Integral representation of FrPDO are obtained. The fractional powers of Hankel-type integral transformations are used in the solution of some partial differential equations.