On Certain Analogues of Noor Integral Operators Associated with Fractional Integrals

Abstract

In this paper, we employ a $q$-Noor integral operator to perform a $q$-analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the $q$-fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the $q$-fractional integral operator and obtain some applications for the differential subordination.