On a terminal value problem for a generalization of the fractional diffusion equation with hyper‐Bessel operator
https://doi.org/10.1002/mma.6087Publisher, magazine: ,
Publication year: 2020
Lưu Trích dẫn Chia sẻAbstract
In this paper, we consider an inverse problem of recovering the initial value for a generalization of time‐fractional diffusion equation, where the time derivative is replaced by a regularized hyper‐Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill‐posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.
Tags: fractional Tikhonov regularization, hyper-bessel operator, time-fractional diffusion equation
Các bài viết liên quan đến tác giả Nguyễn Huy Tuấn
A nonhomogeneous backward heat problem: regularization and error estimates
A nonlinear case of the 1-D backward heat problem: regularization and error estimate
Regularization and error estimates for nonhomogeneous backward heat problems
Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems
An approximate solution for a nonlinear biharmonic equation with discrete random data
Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
Regularization of a terminal value problem for time fractional diffusion equation
Approximation of mild solutions of a semilinear fractional differential equation with random noise