A generalized operator involving the $q$-hypergeometric function

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Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator (2018, methodology): “Moreover, in recent years, such q-calculus operators as the fractional q-integral and fractional q-derivative operators were used to construct several subclasses of analytic functions (see, for example, [1], [6], [26], [27], [33], [35], [36], [37] and [38]).”
Some Applications of a New Integral Operator in q-Analog for Multivalent Functions (2019, methodology): “Recently, new thoughts by Maslina in [17] were used to create a novel differential operator called generalized q-differential operator with the help of q-hypergeometric functions where the authors conducted an in-depth study of applications of this operator.”
Convolution Properties for Certain Classes of Analytic Functions Defined by -Derivative Operator (2014, background): “Mohammed and Darus [9] studied approximation and geometric properties of these qoperators in some subclasses of analytic functions in compact disk.”
Some Subordination Results on -Analogue of Ruscheweyh Differential Operator (2014, background): “Very recently, other q-analogues of differential operators have been introduced in [9]; see also ([10, 11]).”