Some Applications of Analytic Functions Associated with q -Fractional Operator

Nazar Khan, Shahid Khan, Qin Xin, Fairouz Tchier, Sarfraz Nawaz Malik () and Umer Javed
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Nazar Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
Shahid Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
Qin Xin: Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark
Fairouz Tchier: Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
Sarfraz Nawaz Malik: Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan
Umer Javed: Department of Electrical and Computer Engineering, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan

Mathematics, 2023, vol. 11, issue 4, 1-17

Abstract: This paper introduces a new fractional operator by using the concepts of fractional q -calculus and q -Mittag-Leffler functions. With this fractional operator, Janowski functions are generalized and studied regarding their certain geometric characteristics. It also establishes the solution of the complex Briot–Bouquet differential equation by using the newly defined operator.

Keywords: analytic functions; quantum (or q -) calculus; fractional q -derivative operator; q -Mittag-Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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