On a backward problem for fractional diffusion equationwith Riemann‐Liouville derivative

Authors: Nguyễn Huy Tuấn, Nguyen Hoang Tuan, Dumitru Baleanu, Trần Ngọc Thạch, Nguyễn Huy Tuấn,

https://doi.org/10.1002/mma.5943

Publisher, magazine: ,

Publication year: 2020

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Abstract

In the present paper, we study the initial inverse problem (backward problem)for a two‐dimensional fractional differential equation with Riemann‐Liouvillederivative. Our model is considered in the random noise of the given data.We show that our problem is not well‐posed in the sense of Hadamard. A trun-cated method is used to construct an approximate function for the solution(called the regularized solution). Furthermore, the error estimate of the regu-larized solution in L2and Hτnorms is consi dered and illustrated by numericalexample

Tags: backward problem, fractional diffusion equation, random noise, regularized solution