Some Applications of Analytic Functions Associated with <i>q</i>-Fractional Operator

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 <i>q</i>-) calculus
• fractional <i>q</i>-derivative operator
• <i>q</i>-Mittag-Leffler function