A new admissible function class and subordinate technique for fractional operator imposed by wright-type function

The availability of fractional operators is wide-ranging in various scientific disciplines. In complex analysis, numerous findings have been inferred in terms of Fractional Calculus alongside Special Functions. In 2010s, the version of differential subordination concerning the third order has been systemically proposed to play a decisive role in Geometric Function Theory. This note presents the fractional derivative operator formulated by generalized Wright-type functions. Based on the operator described in this novel, recurrence relations are also yielded. The third -order analytical admissibility technique is utilized to discuss the subordination problem. Some admissible classes of regular functions and differential subordination outcomes related to this new operator are examined. Moreover, a variety of differential inequalities are derived as implementations of these outcomes. Furthermore, several corresponding differential supordination outcomes containing this considered operator are gained. Additionally, the differential sandwich-type outcome is also investigated.