Majorization in Analytic Functions Among Distinct Classes Defined by Modified Tremblay Fractional Operator

This paper presents and investigates three distinct kinds of analytic functions described by the Modified Tremblay Fractional Operator: IΥ[A,B], QΥ[A,B], and PΥ[A,B]. We give a detailed knowledge of these unique categories features by exploring majorization difficulties within them. By means of a careful analysis of majorization phenomena, we present a range of novel findings that demonstrate the significance of parameter specialisation in these classes. This work greatly expands our understanding of analytic functions and improves the field of mathematical analysis as a whole. To sum up, this study offers a comprehensive investigation of new analytic function classes, clarifies certain aspects of majorization, and makes significant contributions that broaden our understanding of complex analysis and geometric function theory.