A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients

Rabha W. Ibrahim, Rafida M. Elobaid and Suzan J. Obaiys
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Rabha W. Ibrahim: Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
Rafida M. Elobaid: Department of General Sciences, Prince Sultan University, Riyadh 12345, Saudi Arabia
Suzan J. Obaiys: School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya 62200, Malaysia

Mathematics, 2020, vol. 8, issue 5, 1-13

Abstract: Quantum inequalities (QI) are local restraints on the magnitude and range of formulas. Quantum inequalities have been established to have a different range of applications. In this paper, we aim to introduce a study of QI in a complex domain. The idea basically, comes from employing the notion of subordination. We shall formulate a new q-differential operator (generalized of Dunkl operator of the first type) and employ it to define the classes of QI. Moreover, we employ the q-Dunkl operator to extend the class of Briot–Bouquet differential equations. We investigate the upper solution and exam the oscillation solution under some analytic functions.

Keywords: differential operator; unit disk; univalent function; analytic function; subordination; q-calculus; fractional calculus; fractional differential equation; q-differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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