Applications of differential subordination and superordination theorems to fluid mechanics involving a fractional higher-order integral operator
J. Morais, Hanaa M. Zayed
Abstract
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.