Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain

1 Cloud Computing Center, University Malaya, 50603, Malaysia
2 Mathematical Sciences, Kent State University, Burton, Ohio 44021-9500, USA

Special Issues: Initial and Boundary Value Problems for Differential Equations

Very recently, a new local and limit-based extension of derivatives, called conformable derivative, has been formulated. We define a new conformable derivative in the complex domain, derive its differential calculus properties as well as its geometric properties in the field of geometric function theory. In addition, we employ the new conformable operator to generalize the Briot-Bouquet differential equation. We establish analytic solutions for the generalized Briot-Bouquet differential equation by using the concept of subordination and superordination. Examples of special normalized functions are illustrated in the sequel.
  Article Metrics


1. D. R. Anderson, D. J. Ulness, Newly defined conformable derivatives, Adv. Dyn. Syst. Appl., 10 (2015), 109-137.

2. D. R. Anderson, E. Camrud, D. J. Ulness, On the nature of the conformable derivative and its applications to physics, J. Frac. Calc. Appl., 10 (2019), 92-135.

3. P. L. Duren, Univalent Functions, New York: Springer-Verla, 2001.

4. A. W. Goodman, Univalent Functions, Florida: Mariner Publishing Co. Inc., 1983.

5. W. Janowski, Some extremal problems for certain families of analytic functions, I. Ann. Polon. Math., 28 (1973), 297-326.    

6. Y. Li, K. H. Ang, G. C. Y. Chong, PID control system analysis and design, IEEE Control Syst. Mag., 26 (2006), 32-41.

7. S. S. Miller, P. T. Mocanu, Differential Subordinations: Theory and Applications, New York: Marcel Dekker, 2000.

8. G. S. Sàlàgean, Subclasses of univalent functions, complex analysis-fifth romanian-finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., 1013 (1983), 362-372.    

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved