Existence of an initial value problem for time-fractional Oldroyd-B fluid equation using Banach fixed point theorem

Authors : Vo Viet TRI

Pages : 523-530

Doi:10.31197/atnaa.943242

View : 13 | Download : 7

Publication Date : 2021-12-30

Article Type : Research Paper

Abstract :In this paper, we study the initial boundary value problem for time-fractional Oldroyd-B fluid equation. Our model contains two Riemann-Liouville fractional derivatives which have many applications, for example, in viscoelastic flows. For the linear case, we obtain regularity results under some different assumptions of the initial data and the source function. For the non-linear case, we obtain the existence of a unique solution using Banach`s fixed point theorem.
Keywords : Time fractional Oldroyd B fluid problem, Riemman Liouville, regularity, Banach fixed point theory