Applications of nonhomogenous Cauchy-Euler fractional $q$-differential equation to a new class of analytic functions

Document Type : Original Article


Kocaeli University, Faculty of Aviation and Space Sciences, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey



In this paper, we define a new general fractional $q$-differential operator and by means of this operator we introduce a new subclass of analytic functions which are the solutions of the nonhomogenous Cauchy-Euler fractional $q$-differential equations. Our aim is to determine upper bounds of Taylor-Maclaurin coefficients for functions belong to this class.


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