Composition Formula for Saigo Fractional q ‐Calculus Operator for the q ‐Analogue of the H‐Function

The purpose of this paper is to investigate key properties of Saigo’s fractional q ‐integral and q ‐derivative operators involving the q ‐analogue of Fox’s H‐function. We establish four main theorems describing the action of Saigo‐type fractional q ‐operators on generalised power functions expressed in terms of the q ‐Fox H‐function. Several special cases and limiting forms that arise naturally from these results are also discussed.