We exhibit applications of the index transforms recently established by the author, which involve modified Bessel and associated Legendre functions as the kernels to solve boundary value problems in a wedge for higher order PDE’s. This class of transformations has a feature in integration with respect to a parameter (index) of the special function. The classical and basic examples are the Kontorovich-Lebedev and Mehler-Fock transforms. Concrete examples are demonstrated.