Properties of Fractional Calculus Operators and Results of Their Applications to The Multiplier Transformations Operator Within a Different Class of Multivalent Functions

Abstract

The summary of this research article is to present and study some of the basic and important properties of fractional calculus by examining their applications, which involve multiplier transformations and other generalized operators.  This is done in light of defining a new class of multivalent functions and distinguishing them by multiplier transformations operator. I study and prove the most important distortion or deformation inequalities, including their inclusion of fractional operators. At the forefront of these results is the determination of the coefficients. In fact, I have already explained most of the previous studies related to the subject. In conclusion, the article provides new approaches to studies presented in previous research on the topic.