On some formulas for fractional integration of one Fox function with five parameters

The study obtained Riemann – Liouville and Erdelyi – Kober formulas for fractional integration of five-parameter special Fox function. The paper gives an integral representation of the function under consideration in terms of the Mellin – Barnes integral, conditions for absolute convergence, and asymptotic expansions both for large and small values of the argument. We obtained the formulas proved, using the above integral representation and known power rules for integration. For partial parameters, we got some well-known elementary and special functions.