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The paper aims to study differential subordination and superordination preserving properties for certain analytic multivalent functions within the open unit disk related to a novel generalized fractional derivative operator for higher-order derivatives. As an application, we provide an explicit construction for the complex potential (the complex velocity) and the stream function of two-dimensional fluid flow problems over a circular cylinder using both vortex and source/sink. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of a source is also a source for a given complex potential. Finally, we present some plot simulations that illustrate the results of this work.