On the Weber type integral equation related to the Weber-Titchmarsh problem

We derive solvability conditions and closed-form solution for the Weber type integral equation, related to the familiar Weber-Orr integral transforms and the old Weber-Titchmarsh problem (posed in Titchmarsh (1924), pp. 15, 16), recently solved by the author. Our method involves properties of the inverse Mellin transform of integrable functions. The Mellin-Parseval equality and some integrals, involving the Gauss hypergeometric function, are used.