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The main aim of this book is to present new exact analytical solutions for different motions of non-Newtonian fluids in which the velocity is given on a part of the boundary and the shear stress on the other part. In chapter 1 some important concepts regarding Newtonian and non-Newtonian fluids, differential and rate type fluids, some constitutive equations, equations of motion, and some integral transforms have been discussed. Then in the next all chapters exact analytical solutions for the velocity field and the shear stress(es) corresponding to some flows in which the velocity is given on a part of the boundary and the shear stress on the other part have been established for different kinds of non-Newtonian fluids as well as some fractional models.