ON TRANSFORMATION OF BASIC HYPERGEOMETRIC FUNCTIONS APPLYING FRACTIONAL q-DIFFERENTIAL OPERATOR

The object of this paper is to establish transformations in which a basic hypergeometric functions can be expressed as an infinite sum of functions of higher order by the application of fractional q-differential operator.Several well known hypergeometric functions and basic Kamp\.{e} de F\.{e}riet function are expressed as an infinite sum of basic hypergeometric functions.Some special cases can be deduced as the application of the main results.