Differential subordination and superordination results for p-valent analytic functions associated with (r,k)-Srivastava fractional integral calculus.

The object of the present paper is to investigate generalizations of the hypergeometric function and Srivastava fractional integral calculus by using a general version of gamma function(namely $\left(r,k\right)$ -gamma function).•Some fundamental results for these new concepts are provided.•We introduced differential subordination and superordination results associated with the defined new fractional integral operator.•Also, we establish sandwich results for $p$ -valent analytic functions involving this operator.•Finally, an application to fluid mechanics is discussed.