Applications of the Neutrosophic Poisson Distribution for Bi-Univalent Functions Involving the Modified Caputo’s Derivative Operator

Abstract

This paper establishes the upper bounds for the second and third coefficients of holomorphic and bi-univalent functions in a family which involves Bazilevic functions and μ-pseudo-starlike functions under a new operator, joining the neutrosophic Poisson distribution with the modified Caputo’s derivative operator. We also discuss Fekete–Szego’s function problem in this family. Examples are given to support our case for the neutrosophic Poisson distribution. The fields of physics, mechanics, engineering, and biology all make extensive use of fractional derivatives.

Keywords

• Bi-univalent functions
• neutrosophic Poisson distribution
• modified Caputo’s derivative operator
• Bazilevic functions
• <i>μ</i>-pseudo-starlike functions
• (<i>G</i>, <i>H</i>) Lucas polynomial