Identifying the initial condition for space-fractional sobolev equation

Abstract

In this work, a final value problem for a fractional pseudo-parabolic equation is considered. Firstly, we present the regularity of solution. Secondly, we show that this problem is ill-posed in Hadamard’s sense. After that we use the quasi–boundary value regularization method to solve this problem. To show that the proposed theoretical results are appropriate, we present an illustrative numerical example. © 2021, Wilmington Scientific Publisher. All rights reserved.