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

Year 2021, , 523 - 530, 30.12.2021

Vo Viet Trı

https://doi.org/10.31197/atnaa.943242

Cited By: 1

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

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