Differential subordination involving generalized Bessel-Maitland function

In this thesis, our primary objective is to establish several subordination results by employing a linear operator that incorporates the normalized form of the generalized Bessel-Maitland functions. The Bessel-Maitland functions, known for their generalization of classical Bessel functions, possess a wide range of applications in mathematical analysis, particularly in the theory of special functions and fractional calculus. By utilizing their normalized form within a suitable operator framework, we are able to explore new aspects of analytic function theory. The subordination results presented herein are derived through a detailed investigation of certain carefully defined classes of admissible functions. These classes consist of analytic functions that satisfy specific structural and geometric conditions, which ensure the validity of the subordination relationships under consideration. The notion of admissibility plays a central role in the development of our results, as it allows for a unified treatment of various function classes within the analytic setting. Through this approach, we not only extend existing results in the literature but also contribute new insights into the behavior of analytic functions under the influence of the proposed operator. The theoretical findings are further supported by illustrative special cases, which demonstrate the applicability and generality of the results obtained.