On some properties of one special function

In the paper, some properties of one particular case of the special Fox function are studied. In particular, an autotransformation formula and its integral representation for some parameters are obtained. The Mellin transform formula is given. In terms of the function under study, solutions to boundary value problems for a differential equation with a Bessel operator acting with respect to a spatial variable and a partial derivative of a fractional order with respect to a time variable were previously written out. When proving the results obtained, the well-known properties of the Euler gamma function, the Wright function, and the properties of the Mellin transform were used.