On a terminal value problem for a generalization of the fractional diffusion equation with hyper‐Bessel operator

Authors: Nguyễn Huy Tuấn, Lê Nhật Huynh, Nguyễn Hữu Cần, Dumitru Baleanu, Nguyễn Huy Tuấn,

https://doi.org/10.1002/mma.6087

Publisher, magazine: ,

Publication year: 2020

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Abstract

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