Application of the Neutrosophic Poisson Distribution Series on the Harmonic Subclass of Analytic Functions using the Salagean Derivative Operator

The authors explore the innovative application of the Neutrosophic series, particularly the Neutrosophic Poisson Distribution Series (NPDS), to investigate various indeterminacy or uncertainties inherent in the classical univalent harmonic function class. The Neutrosophic Poisson Distribution Series is equipped with a Salangean derivative operator and convoluted with analytic univalent harmonic function class to derive new properties, such as inclusion relation, and coefficient inequalities for star-likeness. The results obtained demonstrate the effectiveness of this approach in capturing the inherent uncertainties and complexities associated with harmonic functions. There are several other areas of importance of our results that can be unlocked by computer engineers, scientists, and other experts. In this investigation, some of these indeterminacy and complexities are revealed using graphs by employing Python software tools. This novel integration enhances the analytical techniques available and opens a new stairway for future research in neutrosophic series and geometric function theory.