Third-Order Differential Subordination and Superordination Results for p-Valent Analytic Function Involving Fractional Derivative Operator

Tayyah A. S., Atshan W. G., YALÇIN TOKGÖZ S.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.70118
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: fractional calculus, p-valent functions, third-order differential subordination and superordination
  • Bursa Uludag University Affiliated: Yes

Abstract

We introduce a concept that generalizes the fractional calculus (differentiation and integration) in the complex domain using the Mellin transform. Special cases that lead to the well-known classical forms are discussed. A real-case example, along with a corresponding plot, is provided for illustration. The fractional derivative mentioned above is utilized to present applications to the differential subordination results of Antonino and Miller, as well as the differential superordination results of Tang et al. for (Formula presented.) -valent analytic functions, ultimately leading to sandwich-type results. Finally, we highlight the potential application of this topic in fluid mechanics.