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In this paper, we aim to introduce some geometric properties of analytic functions by utilizing the concept of fractional entropy in a complex domain. We extend the fractional entropy, type Tsallis entropy in the complex z-plane, by using some analytic functions. Established by this diffusion,we state specic new classes of analytic functions (type Schwarz function). Other geometric properties are validated in the sequel. Our development is completed by the Euler form Lemma and Jack Lemma.

ON NEW CLASSES OF ANALYTIC FUNCTIONS IMPOSED VIA THE FRACTIONAL ENTROPY INTEGRAL OPERATOR