Export file:

Format

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

Content

• 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

## Abstract    Full Text(HTML)    Figure/Table    Related pages

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.
Figure/Table
Supplementary
Article Metrics

Citation: Rabha W. Ibrahim, Jay M. Jahangiri. Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain. AIMS Mathematics, 2019, 4(6): 1582-1595. doi: 10.3934/math.2019.6.1582

References

• 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.

• 1. Rabha W. Ibrahim, Chandrashekhar Meshram, Samir B. Hadid, Shaher Momani, Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator, Journal of Ocean Engineering and Science, 2019, 10.1016/j.joes.2019.11.001
• 2. Rabha W. Ibrahim, Rafida M. Elobaid, Suzan J. Obaiys, Symmetric Conformable Fractional Derivative of Complex Variables, Mathematics, 2020, 8, 3, 363, 10.3390/math8030363
• 3. Hemant Kumar Nashine, G. S. Saluja, Rabha W. Ibrahim, Some fixed point theorems for $(\psi -\phi )$-almost weak contractions in S-metric spaces solving conformable differential equations, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660-020-02386-w
• 4. Rabha W. Ibrahim, Rafida M. Elobaid, Suzan J. Obaiys, A new model of economic order quantity associated with a generalized conformable differential-difference operator, Advances in Difference Equations, 2020, 2020, 1, 10.1186/s13662-020-02670-5
• 5. Rabha W. Ibrahim, Rafida M. Elobaid, Suzan J. Obaiys, A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients, Mathematics, 2020, 8, 5, 794, 10.3390/math8050794
• 6. Rabha W. Ibrahim, Geometric process solving a class of analytic functions using q-convolution differential operator, Journal of Taibah University for Science, 2020, 14, 1, 670, 10.1080/16583655.2020.1769262
• 7. Rabha W. Ibrahim, Dania Altulea, Controlled homeodynamic concept using a conformable calculus in artificial biological systems, Chaos, Solitons & Fractals, 2020, 140, 110132, 10.1016/j.chaos.2020.110132